Question

In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 4 boys and 5 girls are competing, how many different ways could the six medals possibly be given out?

Answer 1

1,440

Step-by-step explanation

We have that 4 boys are competing and also 5 girls are competing. 3 medals are given to the boys and 3 medals are given to the girls.

For the boys, the gold medal can be awarded to one of 4 boys, then the silver medal can be awarded to 3 boys because 1 of them already got the gold medal. Finally, the bronze medal can be awarded to one of 2 boys, since the gold and silver medals are already taken. The number of ways the medals can be given to the boys is,

`permutations_(boys)=4\cdot3\cdot2=24`

This situation is similar for the girls, but in this case, there are 5 girls in total,

`permutations_(girls)=5*4*3=60`

The total ways the six medals can be given is,

`permutations_(boys)* permutations_(girls)=24*60=1,440`

Hence, there are 1,440 ways to give the six medals to the 4 boys and 5 girls.