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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 ______.
Options
1440
144
7!
4C4 × 3C3
Solution
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is 144.
Explanation:
Total number of letters in the ‘ARTICLE’ is 7 out which A, E, I are vowels and R, T, C, L are consonants
Given that vowels occupy even place
∴ Possible arrangement can be shown as below
C, V, C, V, C, V, C i.e. on 2nd, 4th and 6th places
Therefore, number of arrangement = 3P3 = 3! = 6 ways
Now consonants can be placed at 1, 3, 5 and 7th place
∴ Number of arrangement = 4P4 = 4! = 24
So, the total number of arrangements = 6 × 24 = 144.
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