how many ways can the word "Native" be arranged without the vowels being together?

Question

need help with data management

 

Answer 1

Cameron:

 

You can think of this problem in two parts:

 

First think of how many ways you can arrange 3 vowels and 3 consonants:  There are 6 permutations for the vowels (aei, aie, eai, eia, iae, iea) and each would then have 6 permutations for the consonants (ntv, nvt, tnv, tvn, vnt, vtn) for a total of 36 permutations (6 x 6).

 

The second part is to think of the placement of the vowels:  Because they cannot be in consecutive positions, there are 4 ways you can arrange the vowels (alternate positions 1,3,5 or 2,4,6 or with consecutive consonants 1,3,6 or 1,4,6).

 

This should give a total of 144 (36 x 4) ways.

 

- Rob