Permutations P(n,r) - One Line Questions

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