00:01
So in this problem, we're told that a code consists of five letters or five characters in all.
00:05
The first two are letters, and the last three are digits.
00:08
So the first thing we want to do in part a is figure out, well, how many total codes could there be? so i usually start this by putting in the number of places we have, which is five.
00:17
Now, in this case, we have no restrictions.
00:19
So the first two have to be letters.
00:21
Well, remember, there's 26 letters in the alphabet.
00:23
So there's 26 different ways for these two first positions.
00:27
Now, the last three have to be digits.
00:30
Well, the digits we have are between zero and nine, so there's ten of them.
00:33
And again, because we have no restrictions, that means there's ten possible choices for each.
00:37
So now, to figure out the total, all we do is we multiply these together.
00:41
So we have 26 times 26 times 10 times 10, which would give us a total of 676 ,000 different codes we could possibly have.
00:51
All right.
00:52
Now, in part b, we're starting to have some restrictions.
00:55
It says codes would distinct the letters.
00:57
So again, we have the five different ways.
01:00
And so there's only a restriction on our letters.
01:02
They have to be different.
01:04
Well, there'd be 26 different ways to pick the first one...