In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 9 boys and 4 girls are competing, how many different ways could the six medals possibly be given out?
Question
In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 9 boys and 4 girls are competing, how many different ways could the six medals possibly be given out?
Solution
To solve this problem, we need to calculate the number of ways the medals can be given out separately for boys and girls, and then multiply these two numbers together.
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For the boys: There are 9 boys competing for 3 medals. The number of ways to give out the medals is the number of permutations of 9 items taken 3 at a time. This is calculated as 9P3 = 9! / (9-3)! = 987 = 504.
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For the girls: There are 4 girls competing for 3 medals. The number of ways to give out the medals is the number of permutations of 4 items taken 3 at a time. This is calculated as 4P3 = 4! / (4-3)! = 432 = 24.
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Multiply the number of ways for boys and girls: The total number of ways to give out the medals is 504 (for boys) * 24 (for girls) = 12096.
So, there are 12096 different ways the six medals could possibly be given out.
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