# Math Help - Combinatorics Application Word Arangement

1. ## Combinatorics Application Word Arangement

Copy of question text:
The letters of the words 'MATHS IS THE BEST' are to be arranged in a row. The number of ways this can be done if the consonants are to be together is...
I don't understand how to get the answer.
I got as far as:

$\frac{2!10!4!}{?}$

The answer should be 1 209 600.

2. I disagree with the given answer.
I think that whoever worked that out did not count the two E’s.

The number of ways to arrange the string $A\boxed{C}EEI$ is $\dfrac{5!}{2}$.
The group of consonants, $\boxed{C}$, can be arranged in $\dfrac{10!}{2\cdot 3!\cdot 3!}$ ways.

3. I got the same answer as Plato.

4. I completely agree with Plato . . .
. . with his reasoning, his answer, and his suspicion.

5. Whao, no wonder why. Thanks.