Permutations and Combinations 3 Question 2

2. A committee of 11 members is to be formed from 8 males and 5 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

(2019 Main, 9 April I)

(a) m=n=68

(b) m+n=68

(c) m=n=78

(d) n=m8

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Answer:

Correct Answer: 2. (c)

Solution:

  1. 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

=(8C6×5C5)+(8C7×5C4)+(8C8×5C3)=(28×1)+(8×5)+(1×10)=28+40+10=78

and n= number of ways when there is at least 3 females

=(5C3×8C8)+(5C4×C7)+(5C5×C6)=10×1+5×8+1×28=78

So, m=n=78



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