Permutation and Combination
Permutation and Combination - Important Points
| 21. | A box contains 2 white balls, 5 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw? |
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A. 135
B. 145
C. 70
D. 85
View Answer Discuss Work SpaceAnswer: option b
Explanation:
No of ways of drawing at least one black ball = (drawing 1 black AND 2 others) OR (drawing 2 black AND 1 other) OR (drawing 3 blacks )
= 5C1 X 6C2 + 5C2 X 6C1 + 5C3 = 75 + 60 + 10 = 145
| 22. | In a party, every guest shakes hand with every other guest. If there were total of 66 handshakes in the party, find the number of persons present in the party? |
|---|
A. 12
B. 33
C. 22
D. 11
View Answer Discuss Work SpaceAnswer: option a
Explanation:
For every handshake two persons are required, let the number of persons present in the party be n.
So, nC2 = 66 or n (n-1) / 2 =66
So, n = 12
| 23. | 5 people are to be arranged in a circle. Find the number of ways such that two particular persons never stand together. |
|---|
A. 18
B. 15
C. 12
D. 8
View Answer Discuss Work SpaceAnswer: option c
Explanation:
n people can be arranged in a circle in (n – 1)!
Numbers of ways 5 people are arranged in circle in 4! Ways.
2 particular people come together in 3! × 2! Ways.
Hence, 2 particular people don’t come together in 4! – 3! 2! = 12
| 24. | In how many ways can 6 similar toffees be distributed to 4 children, such that every child receives at least one toffee? |
|---|
A. 10
B. 15
C. 18
D. 12
View Answer Discuss Work SpaceAnswer: option a
Explanation:
Given that every child receives at least one toffee out of 6 similar toffees.
So, the remaining two toffees can be distributed in (n-1)C(r-1) = (6-1)C(4-1) = 5C3 = 10 ways.
| 25. | A child is asked to pick four coins from a bag containing one coin each of Re. 1, 50p, 25p 10p, 5p, 2p and 1p coins. How many different combinations of the coins can he pick? |
|---|
A. 210
B. 36
C. 35
D. 70
View Answer Discuss Work SpaceAnswer: option c
Explanation:
Different coins = Re. 1, 50p, 25p, 10p, 5p, 2p, 1p.
Total number of different coins = 7.
Number of coins to be selected = 7C4 = 35
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