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 3 girls and no boys will be selected?

C. 1/30

Step-by-step explanation:

From the question, we are told that, there are

Girls = 4

Boys = 6

Total number of children = 10

We are told to find the probability of choosing 3 girls and no boy

To solve for this, we would be using the combination formula

C( n, r) = nCr = n!/r ! (n - r) !

Probability of choosing 3 girls out of 4 = 4C3

Probability of a total of 3 of the team

members = 10C3

The probability of choosing 3 girls and no boy = 4C3 ÷ 10C3

= 4!/3! (4 -3)! ÷ 10!/3! (10 -3)!

= [4! / 3! × 1! ]÷[ 10!/ 3! × 7!]

= [4 × 3 × 2 × 1/ 3 × 2 × 1 × 1 ] ÷ [ 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ 3 × 2 × 1 × 7 × 6 × 5 × 4 × 3 × 2 × 1]

= [ 4 ] ÷ [ 720/6]

= 4 ÷ 120

= 1/30

Therefore, the probability that 3 girls and no boys will be selected = 1/30