Permutation and Combination
Permutation and Combination - Important Points
| 16. | In how many ways can 3 boys and 4 girls be arranged in a row such that boys occupy at the ends? |
|---|
A. 420
B. 360
C. 840
D. 720
View Answer Discuss Work SpaceAnswer: option d
Explanation:
Two boys can be selected and arranged at the ends in 3P2 ways = 6 ways.
Now the rest five people can be arranged in 5! Ways = 120 ways.
So, the total number of ways = 6 × 120 = 720.
| 17. | Out of 2 Women and 5 Men, a committee of 3 is to be formed. In how many ways can it be formed if at least one woman is to be included in the committee? |
|---|
A. 10
B. 15
C. 25
D. 30
View Answer Discuss Work SpaceAnswer: option c
Explanation:
A Committee can be formed in the following ways:
1 woman AND 2 men OR 2 women AND 1 man i.e.
2C1 X 5C2 + 2C2 X 5C1 = 20 + 5 = 25
| 18. | In how many ways can a dinner be organized with 4 men and 4 women at a circular table so that no two women are adjacent? |
|---|
A. 288
B. 144
C. 72
D. 36
View Answer Discuss Work SpaceAnswer: option b
Explanation:
4 men can be seated at the circular table such that there is a vacant seat between every pair of men in (4-1)! =3! Ways.
Now, 4 vacant seats can be occupied by 4 women in 4! Ways. Hence the required number of seating arrangements = 3! X 4! = 144
| 19. | In how many ways can a group of 4 boys and 2 girls be formed out of a total of 7 boys and 4 girls? |
|---|
A. 210
B. 120
C. 224
D. 420
View Answer Discuss Work SpaceAnswer: option a
Explanation:
Number of ways of forming such a group = 7C4 X 4C2 = 35 x 6 = 210
| 20. | In how many ways 3 children can be selected from a group of 5 boys and 3 girls such that at least 1 boy should be there? |
|---|
A. 55
B. 60
C. 45
D. 30
View Answer Discuss Work SpaceAnswer: option a
Explanation:
We can select (1boy and 2 Girls) or (2 boys and 1 girl) or (3 boys)
Number of ways of forming such a group = 5C1 X 3C2 + 5C2 X 3C1 + 5C3 = 15 + 30 + 10 = 55
Permutation and Combination Questions and Answers FAQ
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