00:01
For this problem, you're asked to find the number of codes that can be made from the given letters, h -e -w -e -r -t -t -t.
00:11
What we really need to do is find the number of distinguishable permutations, right? because if we're writing a code, the code's not going to know whether i'm using the first e or the second e.
00:26
So these e's are the same when we write the code.
00:31
There's no way to make them look different.
00:35
These r's would be the same, and these t's would be the same.
00:40
So let me just write something.
00:43
If we had the letters h -e -w -r -t, all of those are different.
00:52
They're distinguishable.
00:55
There's no confusion in any of those.
00:58
So if i wanted to write the codes for this one, i would just use 5 factorial, because that means i could fill the first space in 5 times the second 4.
01:11
We're not going to use the same letter twice, no repeats, 3, 2, and 1.
01:18
So that would be how i can fill.
01:19
The first letter can go 5 ways, and that's what factorial means...