SOLUTION: There are 6 boys and 6 girls in the finals of a talent contest. A contest is held to pick the top 3 winners in both the boy and girl groups in order of talent. How many different o
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-> SOLUTION: There are 6 boys and 6 girls in the finals of a talent contest. A contest is held to pick the top 3 winners in both the boy and girl groups in order of talent. How many different o
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Question 1162099: There are 6 boys and 6 girls in the finals of a talent contest. A contest is held to pick the top 3 winners in both the boy and girl groups in order of talent. How many different options for winners are there?
Multiple choice answers:
a. 27,000
b. 12,200
c. 14,400
d. 32,000 Answer by solver91311(24713) (Show Source):
In this one, order counts, so you need the Permutations of things taken at a time.
For the boys, there are 6 ways to choose first place and for each of those ways, there are 5 ways to choose second place for a total of 30 ways to choose first and second. Then, for each of those 30 ways, there are 4 ways to choose third place for a total of 120 ways to choose the three top boys in order.
The same calculation for the girls.
For each of the 120 ways to choose the boys, there are 120 ways to choose the girls.
John
My calculator said it, I believe it, that settles it
