The number of ways of arranging the letters o | vedclass

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

Question

(D) The word $LINEAR$ has $6$ distinct letters: $L, I, N, E, A, R$. We want to arrange these letters such that $E$ and $A$ are always together,but $N$

Vedclass · Accepted Answer

$144$

Vedclass · Answer

(D) The word $LINEAR$ has $6$ distinct letters: $L, I, N, E, A, R$. We want to arrange these letters such that $E$ and $A$ are always together,but $N$ and $R$ are not together. First,treat $(EA)$ as a single unit. Now we have $5$ units: $L, I, N, R, (EA)$. The number of ways to arrange these $5$ units is $5! = 120$. Since $E$ and $A$ can be arranged within their unit in $2! = 2$ ways,the total number of arrangements where $E$ and $A$ are together is $120 	imes 2 = 240$. Next,we find the number of arrangements where $E$ and $A$ are together $AND$ $N$ and $R$ are also together. Treat $(EA)$ as one unit and $(NR)$ as another unit. Now we have $4$ units: $L, I, (EA), (NR)$. The number of ways to arrange these $4$ units is $4! = 24$. Within their units,$E$ and $A$ can be arranged in $2! = 2$ ways,and $N$ and $R$ can be arranged in $2! = 2$ ways. So,the number of arrangements where both $(EA)$ and $(NR)$ are together is $24 	imes 2 	imes 2 = 96$. Finally,the number of ways where $E$ and $A$ are together but $N$ and $R$ are $NOT$ together is $240 - 96 = 144$.

The number of ways of arranging the letters of the word $LINEAR$ so that the letters $N$ and $R$ do not come together and $E$ and $A$ come together is

Similar Questions

The number of $5$-letter words that can be formed by using the letters of the word $SARANAM$ is

How many words can be formed using the letters of the word $COURTESY$ such that the first letter is $C$ and the last letter is $Y$?

The number of four-digit even numbers that can be formed using the digits $0, 1, 2,$ and $3$ without repetition is:

How many even numbers of $3$ different digits can be formed from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ (repetition is not allowed)?

In how many ways can the letters of the word "$ASSASSINATION$" be arranged so that all $S$'s are together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module