probability

Submitted by Ej-lp ACayabyab on

A committee of 3 is to be selected from a group of 5 girls and 3 boys. What is the probability that two boys are selected?

The answer in my notes is: 15/56.
I need a solutions on how it came up to 15/56.
Please help..thank you..

KMST Wed, 09/14/2016 - 20:34

There are 8 people that we can tell apart from one another.
You can make 8*7*6 lists of 3 people out of those 8.
If you care who is committee president, who is vice-president and who is secretary,
that is your number of possible committee lists.
If all 3 committee positions are equivalent, you would find that the same 3 people appear (in different order) in 3*2=6 lists,
so there are really 8*7*6/6=8*7=56 different committees that can be formed.
How many committees could you form with 1 girl and two boys?
There are 5 choices for the girl.
There are 3 choices for the two boys (3 ways you can choose which of the 3 boys not to include in the committee).
So with 5 choices for the girl part of the committee,
and 3 choices for the boy part,
you have 3*5=15 ways of forming a committee with two boys and one girl.
So, 15 out of 56 possible committees will be made with 2 boys.
That is 15/56.