Question

Six married couple are sitting in a room. Number of ways in which $4$ people can be selected so that there is exactly one married couple among the four is $N,N$ is a three digit number of the form $abc$ then $(a+b-c)$ equals

Answer 1

$6$ couples $\to 12$ people.

$4$ to be selected.

case (1) $\Rightarrow$ 1 couple only $\Rightarrow$

${(}^6{C}_1).{(}^5{C}_2).2.2$

$=6\times 10\times 2\times 2$ $=240$

case (2) $\Rightarrow 2$ couples $\Rightarrow$

${}^6{C}_2=15$

$\therefore$ total ways $=240+15=255$

$a=2,b=5,c=5$

$\therefore a+b-c=2.$