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Question

The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is

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Solution

In word ARTICLE, there are 3 vowels and 4 consonants.

Total number of letters = 7

Total number of even place =3

There are 3 vowels to be filled in 3 places.

Hence, the number of ways = 3C3=1

The vowels can arrange among themselves in 3!=6 ways.

Now, the 4 consonants can fill the remaining 4 places in 4!=24 ways.

Therefore, total number of ways = 1×6×24=144 ways.


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