00:01
Okay, we have here then a total of eight letters.
00:04
So, and they're all different.
00:08
That's important.
00:10
So the first one then, how many ways can i arrange these eight letters with no restrictions? well, all you do is you have one, two, three, four, five, six, seven, eight locations to fill.
00:27
The first location, you have all eight choices, then seven choices, then seven choices, then seven.
00:32
And so on down to one.
00:36
In other words, eight factorial ways of arranging eight letters.
00:42
And that you work out on a calculator, either manually or just use the math button on the ti 84 plus, press math, or enter eight first, enter eight first, then press math, and with the arrow key, select prob, and then select item number four.
01:04
Factorial enter and we get 40320.
01:11
So 40 ,000, 320 different ways of arranging eight letters.
01:19
Now in part b we are told that the first letter must be a vowel.
01:27
So again, one, two, three, four, five, six, seven, eight.
01:32
And the vowels, there are one, two, three, three, four vowels.
01:39
So four choices for the first location.
01:44
And then one's missing.
01:47
So seven choices here, then six, then five, four, three, two, and one.
01:56
So the answer then here will be four times seven factorial.
02:04
And again, seven factorial.
02:07
I'll do it with the calculator very quickly is 5040.
02:13
So four times times 5040 will be 20 ,160.
02:28
Now the next one is you are told the vowels must occupy the odd number places...