A permutation is an arrangement of objects in which the order is important. A combination is a selection of objects in which the order is not important.
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Practice makes perfect
We have enough money to download only 3 of the 8 songs we want.
Is Order Important?
We will begin by naming the 8 songs with letters: A, B, C, D, E, F, G, and H. Now, let's say we choose a group of 3 songs, A, D, and F. We will list the different orders we choose the songs in.
cc
ADF & AFD
DAF & DFA
FAD & FDA
Notice that we still end up with the same 3 songs, no matter what order we choose them in. Therefore, the order in which we choose the songs is not important, since we are only interested in a set of songs we choose and not their order.
Permutations or Combinations?
A combination is a selection of objects in which the order is not important. Combinations focus on the selected objects. A permutations is a selection of objects in which the order is important. In our Since we are evaluating groups of songs instead of orders of songs, we need to use combinations to evaluate the number of different groups of songs we can buy.
Values of n and r
Let's recall the formula for the number of combinations of n objects taken r at a time, for 0 ≤ r ≤ n.
_nC_r = n!/r! (n-r)!
We are choosing from 8 songs we want to download, so n = 8. We only have enough money to download 3 songs, so r = 3. Let's substitute these values into the formula and evaluate the number of combinations we can buy.
