00:01
So looking at this situation here, we're looking at vanity plates.
00:06
You can use one of 26 letters and numbers, 0 to 9, so there's 36 possibilities here.
00:14
Repetitions are allowed.
00:15
How many custom tags are possible? well, keep in mind, again, we have 26 letters, and we do have 10 numbers, so there are 36 possibilities with character plates that are 6 long.
00:32
So we wind up with 36 to the 6th power for this first solution.
00:38
If repetitions are not allowed, this becomes a permutation question.
00:44
So we have 36 options.
00:49
We are looking at 6 spaces or 6 possibilities.
00:55
So this becomes 36p6.
00:59
For question three, it says repetitions are not allowed and there must be exactly three letters.
01:05
How many custom tags are possible? well, as we look at this situation, we have 26 letters to choose from.
01:15
Repetitions are not allowed.
01:16
We need exactly three letters.
01:18
If we need exactly three letters, we also need exactly three numbers.
01:23
So 26c3 or 26 choose 3 times 10 choose 3 are the number of plates that meet those guidelines.
01:34
Number 4, repetitions are not allowed...