Hi,

Here is a problem I'm having a hard time wrapping my head around.

10 people go to a restaurant to order 10 dishes out of 50 distint dishes. If people can share the dishes among themselves then how many distinct eating experiences are possible?

First of, there are 2 cases for whether repetition is allowed of not. In the first case, if repetition is not allowed then there are^{50}P_{10}distinct experiences, else it is 50^{10}. (Permutation because the order of dishes matters in creating distinct experiences.)

How to consider sharing of the 10 dishes among the 10 people? In the no repetition case, 10 distinct dishes can be shared among 10 people in 10^{10}ways, so the total is^{50}P_{10 }X 10^{10 }? What about the case where when repetition allowed, i.e., all people can have the same dish?

Any help is appreciated.

Thanks