1) The starting lineup for a baseball team consists of nine players. Assuming that each member of a team with 25 players can play each position, in how many different ways can the starting lineup be filled?
2) From a pool of 15 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. In how many different ways can the offices be filled?
3) A pizza shop offers eight toppings. If no topping is used twice, in how many different ways can a three-topping pizza be formed?
1) The number of different ways the starting lineup can be filled is 25P9 = 25!/(16!*9!) = 3,268,760.
2) The number of different ways the offices can be filled is 15P4 = 15!/(11!*4!) = 1365.
3) The number of different ways a three-topping pizza can be formed is 8C3 = 8!/(5!*3!) = 56.