Permutation and Combination
Permutation and Combination - Important Points
| 11. | There are 3 questions in a question paper. If the questions have 4, 3 and 2 answers respectively, find the total number of answers. |
|---|
A. 20
B. 16
C. 24
D. 28
View Answer Discuss Work SpaceAnswer: option c
Explanation:
The total number of solutions = 4 x 3 x 2 = 24
| 12. | In how many ways can 3 prizes be distributed among 4 boys, if no boy gets more than one prize? |
|---|
A. 12
B. 16
C. 24
D. 32
View Answer Discuss Work SpaceAnswer: option c
Explanation:
First prize can be given to any of the 4 boys. Similarly, second prize can be given to any of the remaining 3 boys because the boy who got the first prize cannot receive second prize.
Similarly, third prize can be given to any of the remaining 2 boys
Hence total numbers of ways are 4 X 3 X 2 = 24
Note: This is same as Arrangement of 4 boys taken 3 at a time in a way 4P3 = 24
| 13. | In how many ways can 3 prizes be distributed among 4 boys, when a boy may get any number of prizes? |
|---|
A. 12
B. 64
C. 24
D. 56
View Answer Discuss Work SpaceAnswer: option b
Explanation:
First prize to any one of the 4 boys. Similarly second to any one of the 4 boys, and third as well to any one of the 4 boys = 4 X 4 X 4 = 43 = 64
| 14. | In how many ways can 3 prizes be distributed among 4 boys, when no boy gets all the prizes? |
|---|
A. 64
B. 63
C. 112
D. 60
View Answer Discuss Work SpaceAnswer: option d
Explanation:
since any one of the 4 boys may get all the prizes. So, the number of ways in which a boy gets all the 3 prizes = 4
so, the number of ways in which a boy does not get all the prizes = 4^3 – 4 = 60
| 15. | Out of group of 4 persons 2 particular persons always come together. Find the total number of ways in which this can be done. |
|---|
A. 16
B. 10
C. 14
D. 12
View Answer Discuss Work SpaceAnswer: option d
Explanation:
3! × 2! = 12 we will make the 2 who will come together a single unit so there a three different units.
Hence 3! × 2!
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