# Permutations help

#### Afridi

##### New member

This was asked in a past paper, where the answer given is 720. However, when I approach the question as outlined below I get 10800. Where am I going wrong?

_X_T_N_S_N_

So there are 6P4/2! ways in arranging the vowels and then the consonants can be arranged 5!/2. Multiplying the two gives 10800.

#### Harry_the_cat

##### Senior Member
There are 4 vowels not 6.

#### pka

##### Elite Member
View attachment 13244
This was asked in a past paper, where the answer given is 720. However, when I approach the question as outlined below I get 10800. Where am I going wrong? _X_T_N_S_N_
The number of ways to place the vowels is $$\displaystyle \binom{6}{4}\cdot\left(\frac{4!}{2!}\right)$$

#### Dr.Peterson

##### Elite Member
Both your method and pka's are correct, and give the same answer. The given answer appears to be wrong.