Answer:
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
