From 4 men and 6 ladies, a committee of five is to be selected. The number of ways in which the committee can be formed so that men are in majority is:

Question

Smart Achievers · Accepted Answer

(4)

Number of men = 4

Number of ladies = 6

Committee of 5 such that men are in majority can be formed in the following ways.

Case I: Selecting 4 men and 1 lady

Required ways $= {}^{4}C_{4} \times {}^{6}C_{1} = 1 \times 6 = 6$

Case II: Selecting 3 men and 2 ladies

Required ways $= {}^{4}C_{3} \times {}^{6}C_{2} = 4 \times 15 = 60$

$∴$ Total number of ways $= 6 + 60 = 66$

Solution

Q.
From 4 men and 6 ladies, a committee of five is to be selected. The number of ways in which the committee can be formed so that men are in majority is:

1 68

2 156

3 60

4 66

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