Question

A team of $12$ railway station masters is to be divided into two groups of $6$ each, one for day duty and the other for night duty. The number of ways in which this can be done if two specified persons $A,B$ should not included in the same group is

• A. $420$
• B. $504$
• C. $714$
• D. $924$

Answer 1

The correct option is B $504$

Total ways without restriction $={}^{12}{C}_6\times {}^6{C}_6$
Total ways when $A$ and $B$ are together $=2\times {}^{10}{C}_4\times {}^6{C}_6$
$\therefore$ Total required ways $={}^{12}{C}_6\times {}^6{C}_6-2\times {}^{10}{C}_4\times {}^6{C}_6=504$