1. ## permutation - basic

below the basic question of permutation:

given that 4 letters are chosen from the word PAYMENT,find the number of arrangement that start with a vowel

ans: 2P1 x 6P3 = 240
my ans: 120

any guide?

2. It seems like the question assumes the only vowel can be in the first postition.

Giving $\displaystyle ^2P_1 \times ^6P_3 = 240$

As you may realise you start the 4 letter arrangement with a vowel and have another vowel (as there are 2) in positions 2-4.

3. tq for your post, but i hope u can commnet my ans attached as below:

http://img839.imageshack.us/img839/7452/99010889.jpg

4. Why can't N or T be in the last postition? I think you are calculating combinations not permutations as you should. Are you aware of the difference?

5. it mean what i am doing is combination?

6. Hello, nikk!

Why do they include $\displaystyle Y$ in these problems?
There is always that controversy: "Is $\displaystyle Y$ a vowel?"

Given that 4 letters are chosen from the word PAYMENT,
If $\displaystyle Y$ is a vowel: .$\displaystyle \;\underbrace{\text{vowel}}_3 \text{ - } \underbrace{\text{any}}_6 \text{ - } \underbrace{\text{any}}_5 \text{ - }\underbrace{\text{any}}_4 \;=\;360$
If $\displaystyle Y$ is not a vowel: .$\displaystyle \;\underbrace{\text{vowel}}_2 \text{ - } \underbrace{\text{any}}_6 \text{ - } \underbrace{\text{any}}_5 \text{ - }\underbrace{\text{any}}_4 \;=\;240$