Permutations or Combinations? Combinations Answer: 495
Practice makes perfect
We want to find how many ways there are to select 4 out of 12 members from the math team. Note that, in this case, the order is not important. Thus, the situation involves combinations. To calculate the answer, we will use the formula for combinations of n objects taken r at a time, for 0 ≤ r ≤ n.
_n C_r = _n P_r/r! ⇔ _n C_r = n!/r!(n-r)!
In our exercise, n=12 and r=4. Let's substitute these values into the above formula.
There are 495 ways to select 4 out of 12 members from the math team.
Alternative Solution
Using the calculator
We can evaluate the number of combinations _(12)C_4 by using the graphic calculator. To do so, we have to start by entering the number of people in the math team, which is equal to 12.
Next, we push MATH and scroll right until we reach PRB. Then, we scroll down to the third row and push ENTER.
Finally, by entering the number of people to be chosen for the team and hitting ENTER, we can calculate the number of combinations.
