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In word 'ALLAHABAD' how many of them vowels occupy the even po

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In word 'ALLAHABAD' how many of them vowels occupy the even positions?

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In word 'ALLAHABAD' how many of them vowels occupy the even positions?

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Text solutionVerified

There are 4 vowels and all are alike i.e. A's. Also, there are 4 even places viz 2nd, 4th, 6th and 8th. So these 4 even places can be occupied by 4 vowels in

\frac{4 !}{4 !} = 1

way. Now, we are left with 5 places in which5 letters, of which two are alike (2L's) and other distinct, can be arranged in

\frac{5 !}{2 !}

ways.
Hence, the total number of words in which vowels occupy the even places

= \frac{5 !}{2 !} = \frac{5 !}{2 !} = 160

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Question Text	In word 'ALLAHABAD' how many of them vowels occupy the even positions?
Answer Type	Text solution:1
Upvotes	150