If the order in which we choose players in not important, should permutations or combinations be used?
210
Practice makes perfect
We want to find the number of ways we can choose 6 people out of a group of 10 to form a volleyball team. Note that since we are interested only in who will be on the team, the order in which we choose players is not important. This means we want the number of combinations of people. Let's recall the formula for the number of combinations of n objects taken r at a time.
_nC_r = n!/r! (n-r)!
In our case, the total number of people we can choose from is 10, so n = 10. Out of those we choose 6 players for the team, so r = 6. Let's substitute these values into the formula.
We found there are 210 possible ways of choosing 6 people to form the volleyball team out of the group of 10 players.
Alternative Solution
Using a Calculator
We can evaluate the number of combinations _(10)C_6 using a graphic calculator. To do so, we have to start by entering the number of people in the whole group, which in this case is 10.
Next, we push MATH and then scroll right until we reach PRB. Then, scroll down to the third row and push ENTER.
Finally, we can calculate the number of combinations by entering the number of people to be chosen for the team and hitting ENTER.
