Question

In how many different ways can the letters of the word mathematics be arranged

Answer 1

The word MATHEMATICS is an 11 letter word. The word contains 2 M's, 2 A's and 2 T's too.

Hence the total no. of ways of rearranging the letters is,

$\mathrm{\dfrac{10!}{2!\times 2!\times 2!}}\ =\ \dfrac{3628800}{8}\ =}\ \mathbf{\underline{\underline{453600}}}$