1. The problem statement, all variables and given/known data There are 7 different postbox, and 10 identical letters. How many ways can the letters put into the boxes so that there is at least one letter in a postbox? 2. Relevant equations nCr=n!/(n-r)!r! If M,N,O..... things can be done in m,n,o..... ways then ways of doing them together is m*n*o.. 3. The attempt at a solution First I tried to put 7 letters in 7 boxes. It can be done in 1 way only as all the letters are identical. Then I tried to put the rest three letters in the box. Let us mark the letters as A, B and C (just to describe easily). While putting A in a box, for every box there are two solutions, either yes you put or no you don't put. So ways are 2^7. But it also includes that you dont put it any boxes. So, actual ways are 2^7-1. Same for letter B and C. So total ways can be (2^7-1)^3 = 2048383 ways. The problem solution was given a number something less than 100. I think the first step maybe a problem where I said ways to put 7 letters is 1. But then the answer is going to be bigger, not less than 100 anyways. I asked the one who gave this problem about my solution, he couldn't answer. It was on facebook and not on my id. And I don't remember how his solution was. Can anybody tell me where the problem is?