Question

In how many different ways can the letters of the word MASTERPIECE be arranged so that the vowels always come together?​

Answer 1

(D) Treating (AIE). i.e., all the vowels together as one letter. Therefore, the word capital,

i.e., TRNR (AIE) can be arranged in

2

5!

ways.(since R is repeated)

Since (AIE) can also be arranged in 3! ways, therefore, required number of ways

=

2

5!

×3!=

2

120×6

=360

Answer 2

Given,

The word 'MASTERPIECE' is given.

To find,

We have to find the number of different ways by which the letters of the word MASTERPIECE be arranged so that the vowels always come together.

Solution,

There are 100800 different ways by which the letters of the word MASTERPIECE be arranged so that the vowels always come together.

We can simply find the number of ways by which letters of the word MASTERPIECE be arranged so that the vowels always come together by using the concepts of Permutations.

The vowels in the word MASTERPIECE are A, E, I, E, E.

Let us consider the letters A, E, I, E, E to be a single word, then

           A E I E E M S T R P C

Since the consonants have no words repeated, and E is repeated 3 three times in vowels, the number of ways is

        = 7! * 5!/ 3!

        = 100800

Hence, there are 100800 different ways by which the letters of the word MASTERPIECE be arranged so that the vowels always come together.