Let "A" be the selection of 3 runners to form the committee. The number of ways to make this selection is

C(5, 3) = 5!/(3!(5-3)!) = 5!/(3!2!) = 10

However, the group may consist of any 3 members from the group of 5 + 8 = 13. Thus the total number of possible outcomes is

C(13,3) = 13!/(3!(13 - 3)!) = 13!/(3!10!) = 22*13 = 286

The probability of selecting a group consisting of runners only is

P(A) = C(5, 3)/C(13,3) =10/286 = 5/143

a) What is the probability that the committee will not be composed of only runners?

the event A and the event "the committee is not composed of only runners" are mutually exclusive thus

1 - P(A) = 1 - 5/143 = 138/143 = 0.9650

the probability is 0.9650.