0

In how many ways can one or more of $5$ letters be posted into $4$ mail boxes,if any letter can be posted into any of the boxes?

Options:

a) $5^4$ b) $5^4-1$ c) $5^5-1$ d) $4^5-1$

My Approach:

A person goes to post his letter in the mail box he can post the Ist letter in any of the $4$ boxes.

Similarly, he can post the second letter in any of the $4$ letterboxes.

By solving for all $5$ letters,I get $5^4-1$. (Subtracted $1$ for no letter to be placed in any $4$ boxes)

Can anyone give me hint if I am wrong?

Roby5
  • 4,287
Jack
  • 752

1 Answers1

1

How about thinking about the problem as follows:

You have four mailboxes, but then you also have a fifth choice of leaving a letter at home. This means that for each letter, you have a total of 5 choices.

You still have to compensate by subtracting 1, as you already know.

Mankind
  • 13,170
  • What is wrong in my approach.Why can't use this? – Jack Oct 01 '15 at 14:50
  • 1
    @Jack First, you probably meant $4^5$ instead of $5^4$, because you are thinking that you have $4$ choices $5$ times ($4\cdot 4\cdot 4\cdot 4\cdot 4$) - but your solution assumes that you have to post each letter in one of the four mailboxes. You don't allow that you leave some letters behind. The problem asks that you post between 1 and 5 of the letters, so you are allowed to leave some of the letters at home. – Mankind Oct 01 '15 at 14:54