Suppose we have 12 women and 4 men. If we divide these 16 people into4 groups of size 4, what is the probability that each group contains a man?

P = 0.0039

Step-by-step explanation:

From Exercise we have 12 women and 4 men.

We calculate the number of combinations of 16 people, to be divided into 4 teams of 4 people each.

{16}_C_{4} · {12}_C_{4} · {8}_C_{4} =

=/frac{16!}{4!· (16-4) !} · / frac{12!}{4!· (12-4) !}· / frac{8!}{4!· (8-4) !}

=1820 · 495 · 105

=94594500

The number of favorable combinations is

{12}_C_{3} · {9}_C_{3} · {6}_C_{3} =

=/frac{12!}{3!· (12-3) !} · / frac{9!}{3!· (9-3) !}· / frac{6!}{3!· (6-3) !}

=220 · 84 · 20

=369600

The probability is 369600/94594500=16/4095=0.0039

P = 0.0039