Q1. The value of ⁸P₃ is:

336
56
512
24

Difficulty: Easy · Topic: Permutations

Solution

⁸P₃ = 8!/(8-3)! = 8!/5! = 8×7×6 = 336.

Q2. The number of ways to choose 3 books from 7 different books is:

210
35
21
120

Difficulty: Easy · Topic: Combinations

Solution

⁷C₃ = 7!/(3!×4!) = 35.

Q3. The value of 10C3 is:

120
130
115
240

Difficulty: Easy-Medium · Topic: Combinations

Solution

10C3 = 10!/(3!(10-3)!) = 120.

Q4. The value of 8C4 is:

70
80
65
140

Difficulty: Easy-Medium · Topic: Combinations

Solution

8C4 = 8!/(4!(8-4)!) = 70.

Q5. The value of 12C5 is:

792
802
787
1584

Difficulty: Easy-Medium · Topic: Combinations

Solution

12C5 = 12!/(5!(12-5)!) = 792.

Q6. The value of 6C2 is:

15
25
10
30

Difficulty: Easy-Medium · Topic: Combinations

Solution

6C2 = 6!/(2!(6-2)!) = 15.

Q7. The value of 9C4 is:

126
136
121
252

Difficulty: Easy-Medium · Topic: Combinations

Solution

9C4 = 9!/(4!(9-4)!) = 126.

Q8. The value of 5P2 is:

25
40
18
20

Difficulty: Easy-Medium · Topic: Permutations

Solution

5P2 = 5!/(5-2)! = 20.

Q9. The value of 6P3 is:

240
120
117
126

Difficulty: Easy-Medium · Topic: Permutations

Solution

6P3 = 6!/(6-3)! = 120.

Q10. The value of 7P2 is:

42
40
84
49

Difficulty: Easy-Medium · Topic: Permutations

Solution

7P2 = 7!/(7-2)! = 42.

Q11. The value of 8P3 is:

333
672
336
344

Difficulty: Easy-Medium · Topic: Permutations

Solution

8P3 = 8!/(8-3)! = 336.

Q12. The value of 9P2 is:

81
70
72
144

Difficulty: Easy-Medium · Topic: Permutations

Solution

9P2 = 9!/(9-2)! = 72.

Q13. The value of 10P3 is:

1440
720
717
730

Difficulty: Easy-Medium · Topic: Permutations

Solution

10P3 = 10!/(10-3)! = 720.

Q14. The value of 10P4 is:

5036
5050
5040
10080

Difficulty: Easy-Medium · Topic: Permutations

Solution

10P4 = 10!/(10-4)! = 5040.

Q15. The value of 12P3 is:

2640
1320
1332
1317

Difficulty: Easy-Medium · Topic: Permutations

Solution

12P3 = 12!/(12-3)! = 1320.

Q16. The value of 8P5 is:

6715
6728
13440
6720

Difficulty: Easy-Medium · Topic: Permutations

Solution

8P5 = 8!/(8-5)! = 6720.

Q17. The value of 7P4 is:

836
840
1680
847

Difficulty: Easy-Medium · Topic: Permutations

Solution

7P4 = 7!/(7-4)! = 840.

Q18. The value of 5C2 is:

7
10
20
15

Difficulty: Easy-Medium · Topic: Combinations

Solution

5C2 = 5!/(2!(5-2)!) = 10.

Q19. The value of 6C3 is:

40
25
17
20

Difficulty: Easy-Medium · Topic: Combinations

Solution

6C3 = 6!/(3!(6-3)!) = 20.

Q20. The value of 7C3 is:

40
35
70
32

Difficulty: Easy-Medium · Topic: Combinations

Solution

7C3 = 7!/(3!(7-3)!) = 35.

Q21. The value of 9C3 is:

81
89
84
168

Difficulty: Easy-Medium · Topic: Combinations

Solution

9C3 = 9!/(3!(9-3)!) = 84.

Q22. The value of 10C5 is:

504
252
249
257

Difficulty: Easy-Medium · Topic: Combinations

Solution

10C5 = 10!/(5!(10-5)!) = 252.

Q23. The value of 12C4 is:

492
500
495
990

Difficulty: Easy-Medium · Topic: Combinations

Solution

12C4 = 12!/(4!(12-4)!) = 495.

Q24. The value of 15C2 is:

110
102
210
105

Difficulty: Easy-Medium · Topic: Combinations

Solution

15C2 = 15!/(2!(15-2)!) = 105.

Q25. The value of 20C3 is:

1137
1140
2280
1145

Difficulty: Easy-Medium · Topic: Combinations

Solution

20C3 = 20!/(3!(20-3)!) = 1140.

Q26. 4C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

4!/(1!(4-1)!) = 4.

Q27. 4C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

4!/(2!(4-2)!) = 6.

Q28. 4C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

4!/(3!(4-3)!) = 4.

Q29. 5C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

5!/(1!(5-1)!) = 5.

Q30. 5C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

5!/(2!(5-2)!) = 10.

Q31. 5C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

5!/(3!(5-3)!) = 10.

Q32. 5C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

5!/(4!(5-4)!) = 5.

Q33. 6C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6!/(1!(6-1)!) = 6.

Q34. 6C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6!/(2!(6-2)!) = 15.

Q35. 6C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6!/(3!(6-3)!) = 20.

Q36. 6C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6!/(4!(6-4)!) = 15.

Q37. 6C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6!/(5!(6-5)!) = 6.

Q38. 7C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7!/(1!(7-1)!) = 7.

Q39. 7C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7!/(2!(7-2)!) = 21.

Q40. 7C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7!/(3!(7-3)!) = 35.

Q41. 7C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7!/(4!(7-4)!) = 35.

Q42. 7C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7!/(5!(7-5)!) = 21.

Q43. 8C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8!/(1!(8-1)!) = 8.

Q44. 8C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8!/(2!(8-2)!) = 28.

Q45. 8C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8!/(3!(8-3)!) = 56.

Q46. 8C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8!/(4!(8-4)!) = 70.

Q47. 8C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8!/(5!(8-5)!) = 56.

Q48. 9C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9!/(1!(9-1)!) = 9.

Q49. 9C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9!/(2!(9-2)!) = 36.

Q50. 9C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9!/(3!(9-3)!) = 84.

Q51. 9C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9!/(4!(9-4)!) = 126.

Q52. 9C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9!/(5!(9-5)!) = 126.

Q53. 10C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10!/(1!(10-1)!) = 10.

Q54. 10C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10!/(2!(10-2)!) = 45.

Q55. 10C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10!/(3!(10-3)!) = 120.

Q56. 10C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10!/(4!(10-4)!) = 210.

Q57. 10C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10!/(5!(10-5)!) = 252.

Q58. 11C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11!/(1!(11-1)!) = 11.

Q59. 11C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11!/(2!(11-2)!) = 55.

Q60. 11C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11!/(3!(11-3)!) = 165.

Q61. 11C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11!/(4!(11-4)!) = 330.

Q62. 11C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11!/(5!(11-5)!) = 462.

Q63. 12C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12!/(1!(12-1)!) = 12.

Q64. 12C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12!/(2!(12-2)!) = 66.

Q65. 12C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12!/(3!(12-3)!) = 220.

Q66. 12C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12!/(4!(12-4)!) = 495.

Q67. 12C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12!/(5!(12-5)!) = 792.

Q68. 13C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13!/(1!(13-1)!) = 13.

Q69. 13C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13!/(2!(13-2)!) = 78.

Q70. 13C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13!/(3!(13-3)!) = 286.

Q71. 13C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13!/(4!(13-4)!) = 715.

Q72. 13C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13!/(5!(13-5)!) = 1287.

Q73. 14C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14!/(1!(14-1)!) = 14.

Q74. 14C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14!/(2!(14-2)!) = 91.

Q75. 14C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14!/(3!(14-3)!) = 364.

Q76. 14C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14!/(4!(14-4)!) = 1001.

Q77. 14C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14!/(5!(14-5)!) = 2002.

Q78. 15C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

15!/(1!(15-1)!) = 15.

Q79. 15C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

15!/(2!(15-2)!) = 105.

Q80. 15C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

15!/(3!(15-3)!) = 455.

Q81. 15C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

15!/(4!(15-4)!) = 1365.

Q82. 15C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

15!/(5!(15-5)!) = 3003.

Q83. 16C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

16!/(1!(16-1)!) = 16.

Q84. 16C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

16!/(2!(16-2)!) = 120.

Q85. 16C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

16!/(3!(16-3)!) = 560.

Q86. 16C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

16!/(4!(16-4)!) = 1820.

Q87. 16C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

16!/(5!(16-5)!) = 4368.

Q88. 3C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

3C0=1.

Q89. 3C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

3C1=3.

Q90. 3C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

3C2=3.

Q91. 3C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

3C3=1.

Q92. 4C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

4C0=1.

Q93. 4C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

4C1=4.

Q94. 4C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

4C2=6.

Q95. 4C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

4C3=4.

Q96. 4C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

4C4=1.

Q97. 5C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

5C0=1.

Q98. 5C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

5C1=5.

Q99. 5C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

5C2=10.

Q100. 5C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

5C3=10.

Q101. 5C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

5C4=5.

Q102. 5C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

5C5=1.

Q103. 6C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6C0=1.

Q104. 6C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6C1=6.

Q105. 6C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6C2=15.

Q106. 6C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6C3=20.

Q107. 6C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6C4=15.

Q108. 6C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6C5=6.

Q109. 6C6 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

6C6=1.

Q110. 7C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7C0=1.

Q111. 7C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7C1=7.

Q112. 7C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7C2=21.

Q113. 7C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7C3=35.

Q114. 7C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7C4=35.

Q115. 7C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7C5=21.

Q116. 7C6 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

7C6=7.

Q117. 8C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8C0=1.

Q118. 8C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8C1=8.

Q119. 8C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8C2=28.

Q120. 8C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8C3=56.

Q121. 8C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8C4=70.

Q122. 8C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8C5=56.

Q123. 8C6 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

8C6=28.

Q124. 9C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9C0=1.

Q125. 9C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9C1=9.

Q126. 9C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9C2=36.

Q127. 9C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9C3=84.

Q128. 9C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9C4=126.

Q129. 9C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9C5=126.

Q130. 9C6 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

9C6=84.

Q131. 10C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10C0=1.

Q132. 10C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10C1=10.

Q133. 10C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10C2=45.

Q134. 10C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10C3=120.

Q135. 10C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10C4=210.

Q136. 10C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10C5=252.

Q137. 10C6 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

10C6=210.

Q138. 11C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11C0=1.

Q139. 11C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11C1=11.

Q140. 11C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11C2=55.

Q141. 11C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11C3=165.

Q142. 11C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11C4=330.

Q143. 11C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11C5=462.

Q144. 11C6 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

11C6=462.

Q145. 12C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12C0=1.

Q146. 12C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12C1=12.

Q147. 12C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12C2=66.

Q148. 12C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12C3=220.

Q149. 12C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12C4=495.

Q150. 12C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12C5=792.

Q151. 12C6 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

12C6=924.

Q152. 13C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13C0=1.

Q153. 13C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13C1=13.

Q154. 13C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13C2=78.

Q155. 13C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13C3=286.

Q156. 13C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13C4=715.

Q157. 13C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13C5=1287.

Q158. 13C6 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

13C6=1716.

Q159. 14C0 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14C0=1.

Q160. 14C1 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14C1=14.

Q161. 14C2 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14C2=91.

Q162. 14C3 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14C3=364.

Q163. 14C4 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14C4=1001.

Q164. 14C5 =

Difficulty: Easy-Medium · Topic: Combinations

Solution

14C5=2002.

Q165. The number of ways to arrange the letters of MISSISSIPPI is:

34650
11!
39916800
2520

Difficulty: Medium · Topic: Arrangements

Solution

11!/(4!×4!×2!) = 39916800/(24×24×2) = 34650. (4 S's, 4 I's, 2 P's, 1 M).

Chapter 7: Permutations & Combinations

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