Question

In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 6 boys and 14 girls are competing, how many different ways could the six medals possibly be given out?

Answer 1

To determine the number of different ways the six medals can be given out, we can consider the choices for each medal individually.

For the first medal:

1. There are 14 girls competing, so any one of them can be awarded the first medal.

2. There are 6 boys competing, so any one of them can also be awarded the first medal.

Since there are no restrictions on who can receive the first medal, there are a total of 14 + 6 = 20 possible choices.

For the second medal:

1. After awarding the first medal, there are 13 girls remaining who can be awarded the second medal.

2. After awarding the first medal, there are 5 boys remaining who can be awarded the second medal.

Again, there are no restrictions, so there are a total of 13 + 5 = 18 possible choices.

For the third medal:

1. After awarding the first two medals, there are 12 girls remaining who can be awarded the third medal.

2. After awarding the first two medals, there are 4 boys remaining who can be awarded the third medal.

Once again, there are no restrictions, so there are a total of 12 + 4 = 16 possible choices.

To find the total number of ways the six medals can be given out, we multiply the number of choices for each medal together:

20 (choices for the first medal) * 18 (choices for the second medal) * 16 (choices for the third medal) = 5760.

Therefore, there are 5760 different ways the six medals can be given out in the running competition.

Explanation:

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