65. Baseball Teams A baseball team has 15 members. Four of the players are pitchers, and the remaining 11 members can play any position. How many different teams of 9 players can be formed?

To determine how many different teams of 9 players can be formed from the baseball team's 15 members, we can approach the problem by breaking it down into two scenarios: teams that include pitchers and teams that do not. 1. **Teams with Pitchers**: If we include at least one pitcher, we have several sub-cases where we can select from 1 to 4 pitchers, combined with players from the remaining 11. 2. **Teams without Pitchers**: Here, we can simply choose all 9 players from the 11 who can play any position. The calculations involve using combinations, which denote the selection of items without regard to the order of selection. The formula for combinations is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of items, r is the number to choose, and "!" denotes factorial. By systematically calculating and adding these combinations, we find the total number of ways to form a team of 9 players. The final answer emerges as the sum of all possible selections from these scenarios!