00:01
In this problem, we are told that a product code has three letters and three numbers, not necessarily together, and with no repeats allowed for the letters and the numbers.
00:12
If we are allowed to use a, b, c, d, or e for the letters, and 35, 6, 7, or 8 for the numbers, our job is to figure out how many codes are possible.
00:25
So we will start by noting that we need to pick three letters out of this set of five.
00:31
So we're going to pick three letters out of five.
00:43
Notice that order matters here because we're doing a product code, and yet repeats are not allowed.
00:50
So we can think of this in terms of the multiplication principle.
00:54
We have three choices to make.
00:56
We can pick any of the five letters for our first choice, then any of the remaining four for our second choice, and any of the remaining three for our third choice.
01:06
Choice for a total of 60, or we can think of this in terms of permutations.
01:14
We can write this as 5 npr 3, which is 5 factorial over 2 factorial.
01:28
And once again, that's 60.
01:32
So there are 60 ways to choose our letters.
01:35
We're choosing three numbers out of the set of 5, so that number will be the same.
01:41
So when we pick three numbers out of the set of five, we will once again get five times four times three or 60.
02:00
And again, we can check that with npr if we like.
02:04
So we've checked, we have chosen our letters, we've chosen our numbers for the code...