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 it is known that coach $D$ will not be on the panel if coach $A$ is there on it?

Answer 1

Total number of coaches $=6$

Number of panels do not contain $D$ if $A$ is present are selected

${=}^5{C}_3{+}^4{C}_2=10+6=16$

Hence the correct answer is $16$