a group of 7 members having a majority of boys is to be formed out of 6 boys and 4 girls. The number of ways the group can be formed is
Answers
Answer:
3
Step-by-step explanation:
6 boys 1 girl
5 boys 2 girls
4 boys 3 girls
A group of 7 members having a majority of boys is to be formed from 6 boys and 4 girls, then the number of ways the group can be formed is 100 .
Step-by-step explanation:
Required formula:
nCr = n!/[(n-r)!r!]
A group is required to be formed of 7 members out of 6 boys & 4 girls provided it consists of majority of boys.
The selections can be done in the following ways:
No. of combinations of 6 boys and 1 girl = ⁶C₆ * ⁴C₁
No. of combinations of 5 boys and 2 girls = ⁶C₅ * ⁴C₂
No. of combinations of 4 boys and 3 girls = ⁶C₄ * ⁴C₃
Thus,
The total number of ways the group of 7 members can be formed is,
= [combinations of 6 boys and 1 girl] + [combinations of 5 boys and 2 girls] + [combinations of 4 boys and 3 girls]
= [⁶C₆ * ⁴C₁] + [⁶C₅ * ⁴C₂ ] + [⁶C₄ * ⁴C₃]
= [{6!/(0!*6!)} * {4!/(3!*1!)}] + [{6!/(1!*5!)} * {4!/(2!*2!)}] + [{6!/(2!*4!)} * {4!/(1!*3!)}]
= [1 * 4] + [6 * 6] + [15*4]
= 4 + 36 + 60
= 100 ways
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