Question

There are $10$ persons including $3$ ladies. A committee of $4$ persons including at least one lady is to be formed. The number of ways of forming such a committee is

• A. 160
• B. 170
• C. 180
• D. 175

Answer 1

Answer: (D)

175

Answer 2

A committee of 4 persons can be formed in following ways,
(i) 3 persons and one ladies
$={ }^{7} C_{3} \times{ }^{3} C_{1}=35 \times 3=105$
(ii) 2 persons and two ladies
$={ }^{7} C_{2} \times{ }^{3} C_{2}=21 \times 3=63$
(iii) 1 person and three ladies
$={ }^{7} C_{1} \times{ }^{3} C_{3}=7 \times 1=7$
$\therefore$ Total number of ways
$=105+63+7=175$
effect on the physical properties, particularly the hardness, malleability and ductility of the
metal.
Interstitial compounds are extremely inert chemically, have high melting points and are
extremely hard