00:01
For this problem, we know that we are looking for the probability that all of the recruits get an incorrect boot size.
00:16
In order for all of the boots to be of an incorrect size, this would be equal to the number of derangements of four items, which is a particular kind of rearrangement or arrangement where none of the elements are in their original position.
00:45
So it's number of derangements divided by the...
00:51
The number of arrangements.
01:08
Now the number of arrangements of four items would be four factorial.
01:14
4 factorial is 4 times 3 times 2 times 1.
01:18
4 times 3 times 2 is 24.
01:24
For the number of derangements, the general formula, which i'll write out here first, i'll note it's often written as sort of like it's almost looks like factorial n or exclamation mark n that's equal to n minus 1, times the number of derangements of n minus 1 plus the number of derangements of n minus 2.
01:57
So we'll have to sort of go through and...
02:00
Oh, actually, pardon me, i'm over -complicating this...