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In how many ways the letters can be arranged such that the vowels in the word ‘VIBEX’ occupy the even positions when placed in order?

In how many ways the letters can be arranged such that the vowels in the word ‘VIBEX’ occupy the even positions when placed in order? Correct Answer 12

We know that,

There are only two even positions in the word, which are 2nd and 4th.

The vowels in the word are I and E.

So, the number of ways the two letters can be arranged in those two members = 2! = 1 × 2 = 2

The rest of the positions are 1st, 3rd, and 5th.

The other consonants are V, B and X.

The number of ways the three letters can be arranged in those 3 positions = 3! = 3 × 2 × 1 = 6

Total number of ways all the letters can be arranged = 6 × 2 = 12

∴ Total number of ways the letters can be arranged are 12

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