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 consonants

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 is $\frac{4!}{2!} = \frac{24}{2} = 12$.There are $5$ possible gaps created by these $4$ consonants (including the ends) where the $2$ vowels can be placed: $\_ L \_ T \_ T \_ R \_$.The number of ways to choose $2$ gaps out of $5$ is $^{5}C_{2} = 10$.The $2$ vowels $(E, E)$ are identical,so they can be arranged in the chosen gaps in $\frac{2!}{2!} = 1$ way.Total number of words = $12 	imes 10 	imes 1 = 120$.

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 $4$-digit numbers are there with no digit repeated?

There are $9$ chairs in a room on which $6$ persons are to be seated. Out of these,one person is a guest who must occupy one specific chair. In how many ways can they sit?

If all permutations of the letters of the word $MASK$ are arranged in the order as in a dictionary,with or without meaning,which one of the following is the $19^{th}$ word?

It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?

Ten chairs are numbered as $1$ to $10$. Three women and two men wish to occupy one chair each. First,the women choose the chairs marked $1$ to $6$,then the men choose the chairs from the remaining. The number of possible ways is

Vedclass Test Series

Exam Paper Generator

Online Exam Module