1)

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include almost one boy, the number of ways of selecting the team is


A) 380

B) 320

C) 260

D) 95

Answer:

Option A

Explanation:

We have 6 girls and 4 boys. To select 4 members (at most one boy)

  i.e. (1 boy and 3 girls ) or (4 girls)

                   =  $^{6}C_{3}.^{4}C_{1}+^{6}C_{4}$            ............(i)

         Now, selection of captain from 4 members= $^{4}C_{1}$                  ...........(ii)

     $\therefore$     Number of ways to select 4 members ( including the selection of a captain , from these 4 members)

           =     $ (^{6}C_{3}.^{4}C_{1}+^{6}C_{4} )^{4}C_{1} $

           =   $(20\times 4  +15)\times 4  =380$