Aschool 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?

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:

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:

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.
 

The probability is 1/2, or 50%.