Permutations help

Afridi

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Aug 14, 2019
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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

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Mar 16, 2016
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There are 4 vowels not 6.
 

pka

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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

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Nov 12, 2017
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Both your method and pka's are correct, and give the same answer. The given answer appears to be wrong.
 
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