Eight people enter into a 100m race.

Question

a.In How many ways can gold, silver, and bronze medals be awarded for the race?

b.What is the probability that one paticular legendary athlete will win the gold medal

Answer 1

a) The first calculation is simply picking 3 winners out of 8=8C3=56. There are 6 ways of arranging the winners in order of gold, silver, bronze, so 56*6=336.

b) Out of the 6 ways of arranging G, S, B (gold, silver, bronze) two of them are GSB, GBS for the 3 winners. So the probability that one particular athlete of the 8 athletes will obtain gold is 1/(56*3)=1/168.