1. ## permutations

With the letters of the word MATEMATIK, how many 9 lettered words can be(meaningfull or meaningless) written starting and ending with a vowel?

My answer is 7.7!/2.2 but it seems to be wrong.

2. ## Re: permutations

Originally Posted by kastamonu
With the letters of the word MATEMATIK, how many 9 lettered words can be(meaningfull or meaningless) written starting and ending with a vowel?
My answer is 7.7!/2.2 but it seems to be wrong.
This is a messy case problem. Break it down into cases.
1) How many both begin and end with an a.
2) How many begin and with an a but end with either an e or i?
3) Double case 2). WHY?
4) How many neither begin nor end with an a?

3. ## Re: permutations

Many Thanks.I got the solution but can't understand the reason of the double case.

4. ## Re: permutations

Originally Posted by kastamonu
Many Thanks.I got the solution but can't understand the reason of the double case.
In case 2) it begins with a, case 3) is ends is a.

5. ## Re: permutations

I seperated others from ie because in IE middle term was different and there were AAs. In other cases there are two vovels in the middle term.

7. ## Re: permutations

Originally Posted by kastamonu
I seperated others from ie because in IE middle term was different and there were AAs. In other cases there are two vovels in the middle term.
1) How many both begin and end with an a.
$7!$

2) How many begin and with an a but end with either an e or i?

Many Thanks.