00:01
All right, so to answer how many different ways can we rearrange the word special using all seven letters? so this can be answered by doing seven factorial or seven with an exclamation point, which means seven times six times five times four times three times two times one.
00:24
And that final answer is 5 ,040.
00:32
So there's 5 ,040 different ways that, you can rearrange the letters using all seven.
00:38
If you want just using four, that's going to be the permutation of seven letters, taking four at a time.
00:49
And this is a little bit different formula.
00:51
You have to do seven factorial over seven minus four factorial, which is seven factorial over three factorial.
01:11
And we can use a shortcut.
01:12
So if i stop 7 factorial at 3 factorial, that will cancel with the 3 factorial on the bottom.
01:22
And you just have to do 7, 6, 5, 4, and you get 840.
01:31
All right, this one's same type of thing.
01:33
So four people in a line is just 4 factorial.
01:38
So that means 4 times 3 times 2 times 1.
01:44
And that is 24...