How many different 11letter words real or imaginary can be f

How many different 11-letter words (real or imaginary) can be from the letters in the word MATHEMETICS?

Solution

It is given that n = 11

Thus, n! = 11x10x9x8x7x6x5x4x3x2x1 = 39,916,800

But letters M, T, & A are repeated twice.

So divide n! by factor of 2x2x2 = 8

Thus the required answer is

= 39,916,800 / 8

= 4,989,600