If each outfit can only be worn by one model and there is no time for any model to wear more than one dress, how many different shows can Elodie put on? (Note: Two shows are considered the same if they contain the same models wearing the same dresses.)


1 Answer

Since there are 3 dresses but there are 5 models, I'm assuming that for each show there will be 3 models who participate and 2 who don't.

We can go a step further and say that we have Dresses 1, 2, and 3. We have models A, B, C, D, and E and by ordering the models, we can have the first model wear dress 1, the second in dress 2, and the third in dress 3.

So now we've set up the problem to be a standard permutation problem:

#P_(n,k)=(n!)/((n-k)!); n="population", k="picks"#