Question

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

Answer 1

Answer:3/7

Explanation:

Its a bit lengthy(a lot actually:) but...

to solve said problem use;

4C2 to represent the girls and 6C2 to represent the boys. This will be multiplied and then further divided by sample space 10C4(because 6+4=10 and 2+2=4).

Thus your expression will look as such.

4C2 * 6C2

/10C2

Remember for each 4C2, and such, use the combination format.

4!/2!(4-2)! * 6!/2!(6-2)!

/10!/4!(10-4)! .... which will equal 3/7.

Hope it helps anyone who needs it.

Answer 2

The correct question is:
What is the probability that 2 girls and 2 boys will be selected?

Solution:
Total number of students = 10
Ways to select a team of 4 students = 10C4 = 210

2 Boys can be selected from 6 boys in ways = 6C2 = 15
2 Girls can be selected from 4 girls in ways = 4C2 = 6

Number of ways to select 2 boys and 2 girls = 15 x 6 = 90

Probability of choosing 2 boys and 2 girls = 90/210 = 3/7

Thus, if 4 team members are selected, the probability of choosing 2 boys and 2 girls will be 3/7