Question

FairPlay Athletics club has six coaches, viz, $A,B,C,D,E$ and $F$. A panel of coaches comprising of three members has to be formed In how many ways can the panel be formed if exactly one among $A$ and $B$ should be included?

Answer 1

We have to find combinations so that only one of $A\xi B$ are included.

Case $I:$ $A$ included , $B$ excluded.

$2$ spots remaining to be filled by $4$ coaches $(C,O,E,F)={}^4{C}_2=6$

Similarly for Case $II:$ $B$ included, $A$ excluded

Combinations $={}^4{C}_2=6$

$\Rightarrow$ Total $=6+6=12.$

Hence, the answer is $12.$