The number of ways in which a committee consisting of 3 men and 2 women,

Question:

The number of ways in which a committee consisting of 3 men and 2 women, can be chose from 7 men and 5 women, is

(a) 45

(b) 350

(c) 4200

(d) 230

Solution:

The selection of 5 members, consisting of 3 men and 2 women from 7 men and 5 women, can be made by selecting 3 men from 7 men and 2 women from 5 available 

$\therefore$ This can be done in ${ }^{7} C_{3} \times{ }^{5} C_{2}$

$=\frac{7 !}{4 ! 3 !} \times \frac{5 !}{3 ! 2 !}$

$=\frac{7 \times 6 \times 5 \times 4 !}{4 ! \times 3 !} r \frac{5 \times 4 \times 3 !}{3 ! \times 2 !}$

$=\frac{7 \times 6 \times 5}{3 \times 4} \times \frac{5 \times 4}{2}$

$=35 \times 10$

$=350$

Hence, the correct answer is option B.

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