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
• E. 155

Answer 1

Answer: (D)

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