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Find the number of ways in which the let...

Find the number of ways in which the letters of word 'MEDICAL' be arranged if A and E are together but all the vowels never come together.

Text Solution

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The correct Answer is:
960
We have letters M,D,C,I,E,I,A
Let us first arrange vowels, which has number of ways 4!.
Five places are created marked as `xx`.
`xx M xx Dxx CxxL xx`
In these five places, we have to arrange vowels A, E, I so that A and E are together but all are not together.
So, we have to arrange AE and I.
Number of ways are `.^(5)C_(2)xx2!xx2!` (as also be arranged in 2! ways)
So, total number of arrangements `=4!xx .^(5)C_(2)xx2!xx2=960`
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