00:01
For this question, we were asked two questions.
00:03
The first is, in how many ways can the letters of the word calculus be arranged? when you have n distinguishable items, the total number of arrangements is n factorial.
00:20
But when you have n items of which n1 are the same and n2 are the same up to nk, then the total number of arrangements is given by this formula.
00:34
It's n factorial, divided by n1 factorial, divided by n2 factorial, and so on, up to k.
00:43
This is supposed to be n subk factorial.
00:48
So in the word calculus, there's a total of eight letters, but there are two c's, two l's, and two u's.
01:01
So using the formula to the right, we have eight factorial, divided by two factorial, to count for the identical c's.
01:13
Times another 2 factorial for the l's, times another 2 factorial for the u's.
01:21
And this comes out to 5 ,040.
01:24
So there are 5 ,040 ways to arrange the letters of the word calculus...