Six girls and four boys have entered the science fair. First, second, and third place awards are to be given out.
What is the probability that exactly one girl and two boys will receive awards? Express your answer as a percent.
A). 10%
B). 14%
C). 18%
D). 22%
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Answers
Given : 6 g ir ls and 4 b o ys entered the science fair.
First, second, and third place awards are to be given
To Find : probability that exactly one g i rl and two b o ys will receive awards
A). 10%
B). 14%
C). 18%
D). 22%
Solution:
G ir ls = 6
B o ys = 4
Total = 10
Three Award
Total ways = ¹⁰P₃ = 10!/7! = 10 * 9 * 8 = 720 ( as all award are different hence order matters here)
1 g ir ls in 6 can be selected in ⁶C₁ = 6 ways
2 b o ys in 4 can be selected in ⁴C₂ = 6 ways
3 Awards can be distributed in 3! = 6 Ways
Total Ways = 6 x 6 x 6 = 216
Probability = 216/720
= 3/10
= 30 %
None of the given options are correct
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