Multiple choice

Out of 6 teachers and four boys, a committee of eight is to be formed. In how many ways can this be done when there should not be less than four teachers in the committee?

  1. 45

  2. 55

  3. 30

  4. 50

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total 10 people (6 teachers, 4 boys). Committee of 8. At least 4 teachers: (4T, 4B) or (5T, 3B) or (6T, 2B). Ways = C(6,4)*C(4,4) + C(6,5)*C(4,3) + C(6,6)*C(4,2) = 15*1 + 6*4 + 1*6 = 15 + 24 + 6 = 45.