Question

A group consists of 6 men and 5 women. three people are selected to attend a conference. in how many ways can 3 people be selected from this group of​ 11? in how many ways can 3 men be selected from the 6​ men? find the probability that the selected group will consist of all men.

Answer 1

1.

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2.

`\displaystyle\binom{6}{3}=(6!)/(3!3!)=(4\cdot5\cdot6)/(2\cdot3)=20`

3.

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Answer 2

Men = 6
Women = 5
Total number = 6+5 = 11

First question:
This is a question of combination.
Total number of selecting 3 people from the group = 11C3 = 11!/[3!(11-3)!]= 165 ways

Second question:
This is question of combination where only men are considered.
Total number of collecting 3 men from 6 men = 6C3 = 6!/[3!*(6-3)!]= 20 ways

Third question:
The probability that the 3 people selected will all be men is given by:
1st selection: 6/11
2nd selection: 5/10
3rd selection: 4/9
The probability = 6/11*5/10*4/9 = 4/33