Ex: 2 people and 2 restaurants - E(X) = 1(.5) + 2(.5) = 1.5 restaurants will be visited on average

EX: 3 people and 3 restaurants - E(X) = 1(1/9) + 2(6/9) + 3(2/9) = 2.11 restaurants will be visited on average

This is simple enough for small values like these. However, I would like to be able to do this for any combination of X and Y and create a table of expected values. For larger numbers I am having trouble determining the probabilities to plug into the expected value formula. When calculating the probabilities, I know that the denominator will always be X^Y but I am really struggling to find a way to calculate the numerator without writing down every possible combination.

My ultimate goal would be to create a table in excel that for any given number of restaurants and people, returns the expected value.

I'm running into a major road block so any help would be appreciated.