The number of words (with or without meaning) | vedclass

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Question

(C) The word "$LETTER$" contains $6$ letters: $L, E, T, T, E, R$.The vowels are $E, E$ and the consonants are $L, T, T, R$.First,arrange the consonant

Vedclass · Accepted Answer

$120$

Vedclass · Answer

(C) The word "$LETTER$" contains $6$ letters: $L, E, T, T, E, R$.The vowels are $E, E$ and the consonants are $L, T, T, R$.First,arrange the consonants $L, T, T, R$. The number of ways to arrange these $4$ letters (where $T$ repeats twice) is $\frac{4!}{2!} = \frac{24}{2} = 12$.Now,to ensure vowels never come together,we place them in the gaps created by the consonants:_ $L$ _ $T$ _ $T$ _ $R$ _There are $5$ available gaps for the $2$ identical vowels $(E, E)$.The number of ways to choose $2$ gaps out of $5$ is $^{5}C_{2} = \frac{5 	imes 4}{2} = 10$.Since the vowels are identical,there is only $1$ way to place them in the chosen gaps.Total number of words = $12 	imes 10 = 120$.

The number of words (with or without meaning) that can be formed from all the letters of the word "$LETTER$" in which vowels never come together is

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