Question

How many ways are there to arrange the word: MATHEMATICS, if the last letter can not be "H", and the first letter must be a vowel?

Answer 1

First of all there are 11 letters. Line them up by vowels and consonants.
A A E I (vowels)
C H M M S T T (consonants)

You know you must begin with a vowel and must not end with H.

See what you can come up with? (There is always the dictionary!)

Sra

Answer 2

3 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2, i think

Answer 3

I GOT IT!!!!!!!

[10!/(2!2!) - (9!/2!2!)]+[(2)(10!/2!2!2!) - [(2)(9!/2!2!2!)]=1632960