- #1
fireflies
- 210
- 12
Homework Statement
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?
Homework 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..
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 don't 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?