Q. 7 E5.0( 2 Votes )

How many permutations can be formed by the letters of the word, ‘VOWELS,’ when

all consonants come together?

Answer :

Given: the word is ‘VOWELS.’


To find: number of words in which consonants always come together


Number of consonants in this word = 4(V, W, L, S)


Now, consider these four consonants as one entity(VWLS together as a single letter)


So, the total number of letters = 3 (VWLS O E)


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 3 things taken all at a time


= P(3, 3)




{ 0! = 1}


= 3!


= 3 × 2 × 1


= 6


Now, 4 consonants which are together as a letter can be arranged in 4! (like WLVS or SWLV)


= 4 × 3 × 2 × 1 = 24 ways


Total number of words in which vowels come together = 24 × 6 = 144


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