We want to find how many ways we can choose a 13-member subcommittee from the 24 members of the U.S. Senate Committee on Finance. Notice that the order in which we choose the members is not important. After the selection, 13 members are in the subcommittee, regardless of the order in which they were chosen.
_nC_r = n!/r! (n-r)!
In the formula for the number of combinations, n is the number of objects taken r at a time, for 0 ≤ r ≤ n. In our case, we are choosing from the 24 members of the U.S. Senate Committee on Finance, so n = 24. Of these, exactly 13 members are chosen for the subcommittee, so r = 13. Let's substitute these values into the formula.
There are 2 496 144 possible ways of choosing a 13-member subcommittee.
Alternative Solution
Using a Calculator
We can evaluate the number of combinations _(24)C_(13) using a graphing calculator. To do so, we have to start by entering the total number of available people to choose from, 24.
Next, we push MATH and then scroll right until we reach PRB. Then, scroll down to the third row and push ENTER.
Finally, by entering the number of members to be chosen and hitting ENTER, we can calculate the desired number of combinations.
