You download 15 music files on your computer and plan to save 7 of them to an
mp3 player. In how many ways can u arrange the songs. I need to know how many
ways anfd if it is a Combination or a Permutation
Whether it is a combination or permutation depends on YOU, as to whether
YOU care what order they are downloaded in or not.
If YOU care what order they are dowloaded in, then it is a permutation.
15 Position 7 = 15P7 = .
That's 3991680 PERMUTATIONS of 15 things taken 7 at a time.
If YOU DON'T care what order they are in, then it is a combination.
15 Choose 7 = 15C3 =
You can cancel all those factors in the bottom into the factors in the top
and you'll always end up with a whole number.
That's only 792 PERMUTATIONS of 15 things taken 7 at a time. It's much
less because you don't care what order they are downloaded in.
Notice that the numerator of the combination formula is the same as the
permutation formula. The denominator of the combination formula takes
away all the different orderings of each set of songs.
Edwin