Question

I. How many ways can the letter of the word Maggie be arranged

Answer 1

Total alphabets in Mathematics : 11

If all the vowels are to come together, we can treat them as a separate big word.

Then, we have

MTHMTCSAEAI

Treating AEAI as one entity, we are left with 8 words that can be arranged in 8!/2!2! ways( dividing because M and T occur twice).

Further AEAI can be arranged in itself in 4!/2! ways.

Therefore, total number of ways the vowels always come together are 8!4!/2!2!2!

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