Practise counting arrangements and selections with repeated objects, fixed positions, adjacency restrictions and case conditions by choosing permutations or combinations correctly.
The Splash Club has 26 members, of whom 16 are swimmers and 10 are divers. No member is both a swimmer and a diver. The club committee consists of 6 of these 26 members.
In how many ways can the club committee be selected if it must include at least 2 swimmers and at least 2 divers?
In a group of 25 athletes, there are 8 sprinters, 5 hurdlers and 12 throwers.
Find the number of different ways in which a team of 6 athletes can be selected if it consists of at least 3 sprinters, at most 2 hurdlers and at most 1 thrower.
A group of 8 athletes chosen from the group of 25 athletes consists of 1 sprinter, 3 hurdlers and 4 throwers. These 8 athletes stand in a row.
How many different arrangements of the 8 athletes are there if the 3 hurdlers do not stand all together?
How many different arrangements of the 8 athletes are there in which there are at least two athletes between any two hurdlers?
