A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them

A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees?

  1. 80
  2. 160
  3. 200
  4. 320

Answer

Out of the 5 girls, 3 girls can be invited in 5C3 ways.

He can invite one, two, three, four or even no boys. Out of 4 boys, he can invite them in the said manner in (2)4 ways.

Thus, the total number of ways is 5C3 × (2)4 = 10 × 16 = 160.

The correct option is B.