Question

Hw 22.2 -Permutations with repetition

There are 6 runners in s race .In how many ways can 3 runners finish in first ,second ,and third to win the gold ,sliver ,and bronze medals ?

Answer 1

The number of ways to choose 3 runners out of 6 is given by the combination formula:

C(6,3) = 6!/(3!3!) = 20

Once we have chosen the 3 runners who will win the medals, we can arrange them in 3 different orders to win gold, silver, and bronze. The number of ways to do this is given by the permutation formula:

P(3,3) = 3! = 6

Therefore, the total number of ways for 3 runners to finish in first, second, and third to win the gold, silver, and bronze medals is:

20 x 6 = 120

So there are 120 ways for the 3 runners to win the medals in the race.