A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including…

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 at most one boy, then the number of ways of selecting the team is
  1. 380
  2. 320
  3. 260
  4. 95

Solution

There are 2 cases-

i. All the 4 are girls

ii. 3 girls and 1 boy

So the answer is 

6C4+6C3. 4C1. 4C1=380     (4C1= No. of ways of selecting captain)

Asked in: JEE Advanced 2016 (Paper 1)

Practice more Permutation Combination questions on Aicharya