Adriana Ayers

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

Beginner2022-06-20Added 19 answers

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 $\textstyle (}\genfrac{}{}{0ex}{}{20}{5}{\textstyle )$

Part 2: your request:

You request to know how many M only can be seated in this table? Answer $\textstyle (}\genfrac{}{}{0ex}{}{17}{5}{\textstyle )$

Part 3: Result

so the answer is:

$\frac{{\textstyle (}\genfrac{}{}{0ex}{}{17}{5}{\textstyle )}}{{\textstyle (}\genfrac{}{}{0ex}{}{20}{5}{\textstyle )}}$

Part 1: the universe:

How many combination of 5 can you form from 20? Answer $\textstyle (}\genfrac{}{}{0ex}{}{20}{5}{\textstyle )$

Part 2: your request:

You request to know how many M only can be seated in this table? Answer $\textstyle (}\genfrac{}{}{0ex}{}{17}{5}{\textstyle )$

Part 3: Result

so the answer is:

$\frac{{\textstyle (}\genfrac{}{}{0ex}{}{17}{5}{\textstyle )}}{{\textstyle (}\genfrac{}{}{0ex}{}{20}{5}{\textstyle )}}$