Question

A school debate team has 4 girls and 6 boys. A total of 3 of the team members will be chosen to participate in the district debate. What is the probability that 1 girl and 2 boys will be selected?

Answer 1

There are 4+6=10 people in the team.
First calculate in how many ways you can choose 3 people from a group of 10 people, using combination:

`(^(10) _3)=(10!)/(3!(10-3)!)=(10!)/(3! * 7!)=(7! * 8 * 9 * 10)/(6 * 7!)=(8 * 9 * 10)/(6)=(720)/(6)=120`
You can choose 3 people in 120 ways.

You can select 1 girl from a group of 4 girls in 4 ways.
Calculate in how many ways you can choose 2 boys from a group of 6 boys:

`(^6 _2)=(6!)/(2! (6-2)!)=(6!)/(2! * 4!)=(4! * 5 * 6)/(2 * 4!)=(5 * 6)/(2)=(30)/(2)=15`
You can choose 2 boys in 15 ways.
Using the rule of product, you can calculate that you can choose 1 girl and 2 boys in 4×15=60 ways.

The probability of choosing 1 girl and 2 boys is the number of ways you can choose 1 girl and 2 boys divided by the number of ways you can choose 3 people from the group.

`P=(60)/(120)=(1)/(2)=50\%`

The probability is 1/2, or 50%.