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A committee of 11 members is to be forme...

A committee of 11 members is to be formed from 8 males and 5 m=females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with atleast 3 females, then

A

m = n = 68

B

m + n = 68

C

m = n = 78

D

n = m - 8

Text Solution

Verified by Experts

The correct Answer is:
C
Since there are 8 males and 5 females. Out of these 13 members committee of 11 members is to be formed.
According to the question, m = number of ways when there is at least 6 males
`= (""^(8)C_(6) xx ""^(5)C_(5)) + (""^(8)C_(7) xx ""^(5)C_(4)) + (""^(8)C_(8) xx ""^(5)C_(3))`
`= (28 xx 1) + (8 xx 5) + (1 xx 10)`
= 28 + 40 + 10 = 78
and n = number of ways when there is at least 3 females
`= (""^(5)C_(3) xx ""^(8)C_(8)) + (""^(5)C_(4) xx ""^(8)C_(7)) + (""^(5)C_(5) xx ""^(8)C_(6))`
`= 10 xx 1 + 5 xx 8 + 1 xx 28 = 78`
So, m = n = 78
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