Question

A baseball team roster consists of 21 players of which 13 are considered active. Answer the following questions using either the permutation or the combination notation.

​ How many ways are there for a manager to select 13 active players from the​ roster?

Answer 1

There are 1,287,084 ways for a manager to select 13 active players from a roster of 21.

Step-by-step explanation:

To find the number of ways a manager can select 13 active players from a roster of 21, we can use the combination formula. The number of ways to select r objects from a set of n objects is given by the formula C(n, r) = n! / (r!(n-r)!), where n! represents the factorial of n. In this case, we need to find C(21, 13) = 21! / (13!(21-13)!).

Using the factorial formula, 21! = 21 x 20 x 19 x ... x 2 x 1, and 13! = 13 x 12 x 11 x ... x 2 x 1. Simplifying the expression C(21, 13) = 21! / (13!(21-13)!) gives us C(21, 13) = 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 / (13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 1,287,084.

Therefore, there are 1,287,084 ways for a manager to select 13 active players from the roster.