2022-06-19

If there are 20 people with 17 men and 3 women and they seat themselves randomly at 4 Tables (A,B,C,D) with 5 people each. With all arrangements being equally likely, what is the probability that no woman sits at table A ?

lorienoldf7

Formulate the question this way: there are 20 people in a room, 17M and 3W. there's a table with 5 seats, what is the probability that only men sit in this table?
Part 1: the universe:
How many combination of 5 can you form from 20? Answer $\left(\genfrac{}{}{0}{}{20}{5}\right)$
You request to know how many M only can be seated in this table? Answer $\left(\genfrac{}{}{0}{}{17}{5}\right)$
Part 3: Result
$\frac{\left(\genfrac{}{}{0}{}{17}{5}\right)}{\left(\genfrac{}{}{0}{}{20}{5}\right)}$