Q. 7 E5.0( 2 Votes )

# How many permutations can be formed by the letters of the word, ‘VOWELS,’ whenall consonants come together?

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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