Question

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

Short answer

The possible number of words is 4989600.

Step-by-step solution

Step 1. Given information.

The given word is "MATHEMATICS".

Each word formed will have 11 letters: 2 M's, 2 A's, 2 T's, 1 H, 1 E, 1 I, 1 C, and 1 S.

Step 2. Concept.

The number of permutations of $n$objects of which $n_1$are of one kind, $n_2$are of a second kind, ..., and $n_k$are of a $kth$kind is given by

$\frac{n!}{n_1!·n_2!·\cdots ·n_k!}$

Where $n=n_1+n_2+\cdots +n_k$.

Step 3. Determine the number of possible words.

Using the above concept, we get

$\begin{array}{rcl}\text{Possible words}& =& \frac{11!}{2!·2!·2!·1!·1!·1!·1!·1!}\\ & =& \frac{11·10·9·8·7·6·5·4·3·2!}{2!·2·1·2·1·1·1·1·1·1}\\ & =& 4989600\end{array}$

The possible number of words is 4989600.