Find the number of ways of arranging the letters of the word “MATERIAL” such that all the vowels in the word are to come together?

Permutations and Combinations 04/11/2020

A. 720
B. 1440
C. 1860
D. 2160

In the word, “MATERIAL” there are three vowels A, I, E.

If all the vowels are together, the arrangement is MTRL’AAEI’.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways of arranging the above letters = 5! * 4!/2!
= (120 * 24)/2 = 1440 ways.

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