K3.2008
How many ways are there to sort the letters T, O, U, R, E, so that there are no vowels that are next to each other?
*For example, T-E-O-R-U cannot be a way of sorting the letter as E and O are both vowels that are next to each other, although E-T-O-R-U is accepted as there are no vowels next to each other.
NOTE: There are no repeats.
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1 solution
In order to make sure that none of the vowels are next to each other, the vowels must be placed as the first, third, and fifth letters. The rest will be the consonant letters.
Therefore the ways to sort the letters are as follows:
For the vowels (1st, 3rd, and 5th), the ways of sorting them are equal to 3 * 2 * 1 (as there are no repeats).
For the consonants (2nd and 4th), the ways of sorting them are equal to 2 * 1 (as there are no equals).
So in conclusion, the amount of ways to sort the letter T-O-U-R-E are equal to 3! * 2! = 12