Question: Find the distinct number of permutations of four letters of the word MATHEMATICS.

The answer is $\dfrac{11P4}{2!^3} = 990$. Is this correct?

This question along with the answer is from a module from my course, so this is all the details that I am able to provide.

My understanding of this question is how many distinct 4 letter words can be formed from the word 'MATHEMATICS'. Therefore, a word like 'MAME' is valid. I know that using 11P4 alone will not suffice because it will say that there are 4 ways to create the 4 letter word MAME from the word 'MATHEMATICS'. So, we I will need to adjust the output of 11P4, and this is where I am stuck. The answer divides 11P4 by $(2!)^3$. I think this represents the 3 non-distinct letters in the word 'MATHEMATICS' (i.e. M,A,T) which have two copies each. Using Sage, the answer I have is 2,454 which is not the same as the answer provided. Here is the code I wrote:

```
#Input according to question
inputQ='M A T H E M A T I C S'.split(' ')

#Same input, but each letter in input is distinct
inputTest='M1 A1 T1 H E M2 A2 T2 I C S'.split(' ')

print inputQ
print inputTest

#Number of letters to form from the given input
choice=4

ansQ=Permutations(inputQ,choice).list()
ansTest=Permutations(inputTest,choice).list()

print 'Total distinct permutations of ' + str(choice) + ' letter word(s) from the word ' + ''.join(inputQ) +':' ,len(ansQ)
print 'If each letter in '+ ''.join(inputQ) + ' were distinct: ', len(ansTest)

```

What if I only want 1 letter? Then the answer would be 8, which I got by manually listing down all possibilities. But what's the general formula for this sort of problem?