Question

There are $6$ men $M_1,M_2,...M_6$ and $5$ women $W_1,W_2,.....W_5$. A committee of 2 women and 3 men is to be formed under the condition that $M_1$ will serve the committee if $M_2$ is present in committee, and $M_2$ will serve the committee if $W_1$ is present in the committee. If the total number of such committees are $16\lambda$, then find the value of $\lambda$.

Answer 1

Total no of ways in which $W1,M2,M1$ are not included is ${}^4{C}_2{\times }^4{C}_3$
only $W1$ is incuded ${}^4{C}_1{\times }^4{C}_3$
only $W1,M2$ is included ${}^4{C}_2{\times }^4{C}_1$
$W1,M1,M2$ are included${}^4{C}_1{\times }^4{C}_1$
So total no ways are $80$

Hence the value of $\lambda =5$