TITLE: The number of words that can be made by permuting the letters of _MATHEMATICS_ is
QUESTION [5 upvotes]: The number of words that can be made by permuting the letters of MATHEMATICS is 
$1) 5040$
$2) 11!$
$3) 8!$
$4) 4989600$
First of all I do not understand the statement of the problem, I would like if some one tell me with an example.

REPLY [4 votes]: I know this has been answered with a result, but no one explained WHY the final formula is 
$$\frac{n!}{n_1!n_2!...n_k!}$$
As described, we have 11 letters, which we divide into: 2 M's, 2 A's, 2 T's, 1 H, 1 E, 1 I, 1C, and 1 S
Next we calculate how many ways there are to place the M's, next A's, etc, and finally sum the outcomes:
$$P= C(11,2)*C(9,2)*C(7,2)*C(5,1)*C(4,1)*C(3,1)*C(2,1)*C(1,1)$$
$$=\frac{11!}{2!9!}*\frac{9!}{2!7!}*\frac{7!}{2!5!}*\frac{5!}{1!4!}*\frac{4!}{1!3!}*\frac{3!}{1!2!}*\frac{2!}{1!1!}*\frac{1!}{1!}$$$$=\frac{11!}{2!2!2!1!1!1!1!1!} = 4989600 $$
I hope this helps for people in need in the future :)