Question

Find the number of ways of forming a committee of 5 members from 6 men and 3 ladies. How
many committees contain at least two ladies.​

Answer 1

SOLUTION

TO DETERMINE

• The number of ways of forming a committee of 5 members from 6 men and 3 ladies.

• The number of committees contain at least two ladies.

EVALUATION

ANSWER TO QUESTION : 1

Here the total number of members

= 6 + 3

= 9

Now we have to form a committee of 5 members

So the total number of committee

$\displaystyle \sf{ = {}^{9} C_5 }$

$= 126$

ANSWER TO QUESTION : 2

Here we have to form a committee of 5 members that contain at least two ladies

This can be done in below to ways

Case : 1 : 3 men and 2 ladies

Case : 2 : 2 men and 3 ladies

In first case total number of committee

$\displaystyle \sf{ = {}^{6} C_3 \times {}^{3} C_2 }$

$= 20 \times 3$

$= 60$

In the second case total number of committee

$\displaystyle \sf{ = {}^{6} C_2 \times {}^{3} C_3 }$

$= 15 \times 1$

$= 15$

Hence the number of committees contain at least two ladies.

= 60 + 15

= 75

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