Question

There are 4 envelopes with different addresses written on them. There are 4 different letters, each of which must go into one of the envelopes. In how many ways can one put the letters into the envelopes such that everyone of the letters goes into the wrong envelope

Answer 1

Okay, so first we have to calculate how many options we have. There's 4 envelopes with different addresses on them, and 4 different letters that go in the envelopes.

So we can use a 4! to calculate this, or
4*3*2*1, or 24 different possibilities. Now, this is wrong.

We have to remember that we want to only count the options where it goes in the WRONG envelope every time. Instead of 4 options per letter, we have 3 since it has to only be the wrong option. So we have to do 3! instead, which is:

3*2*1 or 6.