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
