Q. 6 C5.0( 2 Votes )

# How many different words can be formed from the letters of the word ‘GANESHPURI’? In how many of these words:Are the vowels always together?

Given: the word is ‘GANESHPURI.’

To find: number of words in which vowels are always together

Number of vowels in this word = 4(A, E, I, U)

Now, consider these four vowels as one entity(AEIU together as a single letter) and arrange these letters

So, the total number of letters = 7(AEIU G N S H P R)

Formula used:

Number of arrangements of n things taken all at a time = P(n, n)

Total number of arrangements

= the number of arrangements of 7 things taken all at a time

= P(7, 7)

{ 0! = 1}

= 7!

= 7 × 6 × 5 × 4 × 3 × 2 × 1

= 5040

Now, 4 vowels which are together as a letter can be arranged in 4! (like EAIU or AEUI)

= 4 × 3 × 2 × 1 = 24 ways

Total number of arrangements in which vowels come together = 24 × 5040 = 120960

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