Permutations help

Afridi

New member
Joined
Aug 14, 2019
Messages
5
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_

So there are 6P4/2! ways in arranging the vowels and then the consonants can be arranged 5!/2. Multiplying the two gives 10800.
 
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 \(\displaystyle \binom{6}{4}\cdot\left(\frac{4!}{2!}\right)\)
 
Both your method and pka's are correct, and give the same answer. The given answer appears to be wrong.
 
Top