Question

There are $10$ persons including $3$ ladies. A committee of 4 persons including atleast 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

The correct option is D $175$

A committee pf $4$ 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) $1$ persons and three ladies
${=}^7{C}_1{\times }^3{C}_3=7\times 1=7$
Therefore, total number of ways
$=105+63+7=175$