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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

How many words can be formed out of the letters of the word '$EDUCATION$' such that vowels occupy the odd positions?

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of a man and a woman,is

The sides $AB, BC, CA$ of a triangle $ABC$ have respectively $3, 4$ and $5$ points lying on them. The number of triangles that can be constructed using these points as vertices is

How many triangles can be drawn by using $9$ non-collinear points?

The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module