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In how many ways we can arrange the letters of the the word MANIFEST with vowels in alphabetical order?

Tutor

Only 6! can be the answer and nothing else. The logic is :consider AEI as 1 separate unit ( as one letter). Apart from it, 5 letters are remaining. So, in total there are 6 letters that have to be arranged. These can be arranged in 6! ways.

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Group AEI into one group and treat them as one alphabet. Now you have M, N, F, S, T, (AEI) - 6 alphabets. You can arrange 6 alphabets in 6! ways. So your answer is 6x5x4x3x2x1 = 720 ways

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6!

Competitive Exam Preparation

6!.. Consider AEI as one unit. Then remains 5. Now you need to arrange 6 so ans would be 6!

It is 8!/3! 8! ways all letters are arranged which includes 3! ways AIE can be arranged within themselves. Since they should be in alphabetical order divide by 3!

Mathematics ( Quantitative Aptitude) Trainer

6! ways. AEI can be grouped as 1 and the other 5 words So this can be arranged in 6! ways

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It should be 8!/3!. All 8 letters can be arranged in 8! ways... however AEI can be arranged in only one way.. hence we can treat them as identical letters. So divided by 3!

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calculate using permutation 8!= 8*7*6*5*4*3*2*1

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