# Math Help - Arrangements

1. ## Arrangements

I cant seem to get my head around some of these problems

E.g. In how many ways may the letters of SAUSAGES be arranged if:
the new arrangement must begin with a vowel,

I am right in saying because there are 4 vowels the answer is;

7!
--------- * 4!
2!*3!

2. Originally Posted by SirOJ
E.g. In how many ways may the letters of SAUSAGES be arranged if: the new arrangement must begin with a vowel.
There are to cases: begins with A or else begins with E or U.

It is $\frac{7!}{3!}+2\cdot\frac{7!}{2!\cdot3!}$