Tell whether the possibilities should be counted using a permutation or combination. Then find the number of possibilities.
You have a carrying case that holds four CDs. You want to know in how many ways you can place four of the ten CDs you own into the case.
Answer: 10*9*8*7=5040 permutation...
For the number of combinations, you need to divide that by 4! = 24
There are that many ways of rearranging the same four CDs.
Thank you. Boy I was way off!!! I guess I over think things.
To determine whether permutations or combinations should be used to calculate the number of possibilities, we need to consider whether the order of the items matters.
In this case, the order in which the CDs are placed in the carrying case does matter. For example, placing CD1 in the first slot and CD2 in the second slot is different from placing CD2 in the first slot and CD1 in the second slot.
Since the order matters, we should use permutations to calculate the number of possibilities.
To calculate the number of permutations, we multiply the number of choices for each slot. In this case, there are 10 CDs to choose from for the first slot, 9 CDs for the second slot, 8 CDs for the third slot, and 7 CDs for the fourth slot:
10 * 9 * 8 * 7 = 5040
Therefore, there are 5040 possible ways to place four out of the ten CDs you own into the carrying case.