Permutations P(n,r) - Question Bank

1. How many ways can 6 distinct books be arranged on a shelf if only 4 books are to be displayed?
A) 15
B) 24
C) 360
D) 720
2. Which of the following expressions is NOT a valid representation of P(n, r)?
A) n! / (n-r)!
B) n * (n-1) * ... * (n-r+1)
C) nPr
D) n! / r!
3. If P(n, 4) = 5040, find 'n'.
A) 7
B) 8
C) 9
D) 10
4. What is the value of P(1, 1)?
A) 0
B) 1
C) 2
D) undefined
5. How many permutations are there of the letters in the word 'SEE'?
A) 3
B) 6
C) 3! / 2!
D) 3! / (2! * 1!)
6. If P(n, r) = n! / (n-r)!, what is P(n, n-1)?
A) n!
B) n! / (n-(n-1))!
C) n! / 1!
D) n! * n
7. What is P(5, 2)?
A) 10
B) 20
C) 25
D) 5!
8. If P(n, 2) = 72, find 'n'.
A) 8
B) 9
C) 10
D) 72
9. How many ways can 4 distinct paintings be arranged on a wall from a collection of 6 distinct paintings?
A) 15
B) 24
C) 360
D) 720
10. The number of permutations of 'n' distinct items taken 'r' at a time is given by P(n, r). If r > n, what is P(n, r)?
A) 0
B) 1
C) n!
D) undefined
11. What is the value of P(10, 0)?
A) 0
B) 1
C) 10
D) 10!
12. If P(n, 3) = 336, find 'n'.
A) 6
B) 7
C) 8
D) 9
13. How many different 4-letter arrangements can be made from the letters of the word 'COMPUTER'?
A) 24
B) 5040
C) 10400
D) 120
14. What is P(7, 7)?
A) 1
B) 7
C) 49
D) 5040
15. If P(n, 2) = 56, find 'n'.
A) 6
B) 7
C) 8
D) 56
16. How many ways can you arrange the letters of the word 'GO'?
A) 1
B) 2
C) 3
D) 4
17. The number of permutations of 'n' distinct objects taken 'r' at a time is equal to:
A) n * (n-1) * ... * (n-r)
B) n * (n-1) * ... * (n-r+1)
C) n * (n-1) * ... * (n-r-1)
D) n * (n-1) * ... * 1
18. What is the value of P(6, 3)?
A) 18
B) 120
C) 216
D) 720
19. If P(n, 3) = 210, find 'n'.
A) 5
B) 6
C) 7
D) 10
20. How many different ways can 5 people be seated in a row of 5 chairs?
A) 5
B) 25
C) 60
D) 120
21. Calculate P(5, 5).
A) 1
B) 5
C) 25
D) 120
22. What is the formula for P(n, r) expanded in terms of factorials?
A) n! / r!
B) n! / (n-r)!
C) (n-r)! / n!
D) r! / (n-r)!
23. If P(n, 1) = 5, what is 'n'?
A) 1
B) 4
C) 5
D) 6
24. How many ways can the first, second, and third prizes be awarded to 10 contestants?
A) 10
B) 30
C) 120
D) 720
25. The expression n! / (n-r)! represents:
A) The number of combinations of 'n' items taken 'r' at a time.
B) The number of permutations of 'n' items taken 'r' at a time.
C) The number of ways to arrange 'n' items.
D) The number of ways to choose 'r' items from 'n'.
26. What is the value of P(8, 3)?
A) 24
B) 64
C) 336
D) 512
27. If P(n, 2) = 12, find 'n'.
A) 3
B) 4
C) 5
D) 6
28. How many distinct permutations are there of the letters in the word 'GOD'?
A) 3
B) 6
C) 9
D) 27
29. Evaluate P(4, 4).
A) 1
B) 4
C) 16
D) 24
30. What is the relationship between P(n, r) and P(n, r-1)?
A) P(n, r) = P(n, r-1) * (n-r+1)
B) P(n, r) = P(n, r-1) + (n-r+1)
C) P(n, r) = P(n, r-1) / (n-r+1)
D) P(n, r) = P(n, r-1) * r
31. If P(n, 5) = 720, what is the value of 'n'?
A) 5
B) 6
C) 7
D) 8
32. How many ways can you arrange 3 letters from the word 'MATH'?
A) 12
B) 24
C) 64
D) 81
33. What does P(n, r) signify in combinatorics?
A) The number of ways to choose 'r' items from 'n' without regard to order.
B) The number of ways to arrange 'r' items from 'n' where order matters.
C) The number of ways to select 'n' items from 'r' where order matters.
D) The total number of items available.
34. If P(n, 3) = 60, find 'n'.
A) 4
B) 5
C) 6
D) 10
35. Calculate P(6, 0).
A) 0
B) 1
C) 6
D) 720
36. Which of the following is equivalent to P(n, r)?
A) n! / r!
B) n! / (n-r)!
C) n * (n-1) * ... * (n-r+1)
D) Both n! / (n-r)! and n * (n-1) * ... * (n-r+1)
37. How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition?
A) 60
B) 120
C) 15
D) 20
38. What is the value of P(10, 3)?
A) 30
B) 1000
C) 720
D) 10! / 7!
39. The number of permutations of 'n' distinct objects taken 'r' at a time is denoted by:
A) C(n, r)
B) P(n, r)
C) nPr
D) Both P(n, r) and nPr
40. If P(n, 2) = 30, find 'n'.
A) 5
B) 6
C) 7
D) 30
41. How many permutations are possible for 4 distinct items taken 2 at a time?
A) 4
B) 8
C) 12
D) 16
42. In how many ways can the letters of the word 'CAT' be arranged?
A) 3
B) 6
C) 9
D) 27
43. Evaluate P(5, 3).
A) 15
B) 60
C) 20
D) 125
44. What is P(n, n)?
A) 1
B) n
C) n!
D) 0
45. What is P(n, 1)?
A) 0
B) 1
C) n
D) n!
46. What is P(n, 0)?
A) 0
B) 1
C) n
D) n!
47. If P(n, 4) = 1680, what is the value of 'n'?
A) 5
B) 6
C) 7
D) 8
48. Calculate P(7, 2).
A) 14
B) 49
C) 42
D) 21
49. How many ways can 3 distinct books be arranged on a shelf from a collection of 5 distinct books?
A) 10
B) 60
C) 120
D) 15
50. The notation P(n, r) represents:
A) The number of combinations of 'n' items taken 'r' at a time.
B) The number of permutations of 'n' items taken 'r' at a time.
C) The sum of 'n' and 'r'.
D) The product of 'n' and 'r'.
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