Question

Find the number of combination that can be formed with the letters of the word'MANNER'so that the vowels are always together

Answer 1

Answer:

The total number of ways in which the letters of the word MANNER can be arranged with vowels together will be 120 ways.

Explanation:

There are two vowels in the word MANNER which are A and E, so we will consider this as a single alphabet as AE

So the numbers of alphabets in the words = 5 = M, N, N, R, (AE)

These 5 alphabets can be arranged in 5! ways

out of these alphabets N occur twice, So the ways in which these alphabets can be arranged = 5!/2! = 120/2 = 60

Again since A and E can be arranged in two different ways as AE and EA

Hence the total number of ways in which the letters can be arranged

= 60 x 2

= 120 ways.