(a)[4]
Calculate the number of distinct ways to choose a team of 6 athletes if it contains at least 3 sprinters, no more than 2 hurdlers and no more than 1 thrower.
(b)[3]
From the group of 25 athletes, a set of 8 athletes is made up of 1 sprinter, 3 hurdlers and 4 throwers. These 8 athletes are then arranged in a line. How many distinct arrangements of the 8 athletes are possible if the 3 hurdlers are not all adjacent?
(c)[3]
How many different arrangements of the 8 athletes are there in which every pair of hurdlers has at least two athletes between them?