Question

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?

Answer 1

Answer:

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