Finals for women's Olympics high jumps comes to 6 women. 2 are from Australia, 3 from Poland and 1 from the UK. Determine the number of ways that medals can be awarded if there are no restriction...

Finals for women's Olympics high jumps comes to 6 women. 2 are from Australia, 3 from Poland and 1 from the UK. Determine the number of ways that medals can be awarded if there are no restriction and if the gold is won by the woman from the UK.

Expert Answers
justaguide eNotes educator| Certified Educator

The finalists for the high jump finals are 2 women from Australia, 3 from Poland and 1 from the UK. To determine the number of ways in which the medals can be awarded it should be kept in mind that more than one medal can be won by any country and the order matters.

If there is no restriction the medals to can be awarded to any of the finalists. This can be done in P(6, 3) ways.

`P(6, 3) = (6!)/(3!*3!) = 120`

If the woman from the UK wins the gold, there are two medals that can be won by any of the 5 remaining finalists. The number of ways the medals can be awarded is P(5, 2)

`P(5, 2) = (5!)/(2!*3!) = 20`

The required number of ways in which the medals can be awarded is 120 in the first case and 20 in the second.