Q. 6 C5.0( 3 Votes )

How many differen

Answer :

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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