The number of ways in which the letters of th | vedclass

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

Question

(B) The word $ARRANGE$ consists of $7$ letters: $A, A, R, R, N, G, E$. There are two $A$'s,two $R$'s,and one each of $N, G, E$. The total number of ar

Vedclass · Accepted Answer

$900$

Vedclass · Answer

(B) The word $ARRANGE$ consists of $7$ letters: $A, A, R, R, N, G, E$. There are two $A$'s,two $R$'s,and one each of $N, G, E$. The total number of arrangements is given by: $\frac{7!}{2! 	imes 2!} = \frac{5040}{4} = 1260$. To find the number of arrangements where both $R$'s are together,we treat the pair $(RR)$ as a single unit. Now we have $6$ units: $(RR), A, A, N, G, E$. The number of arrangements of these units is: $\frac{6!}{2!} = \frac{720}{2} = 360$. Therefore,the number of arrangements in which both $R$'s do not come together is: $1260 - 360 = 900$.

The number of ways in which the letters of the word $ARRANGE$ can be arranged such that both $R$ do not come together is

Similar Questions

In how many ways can one send $6$ new-year greeting cards to $4$ people?

While dialing a telephone number,an old man forgets the last two digits,remembering only that these are different. If he dials the last two digits at random,what is the probability that the number is dialed correctly?

How many words can be formed using the letters of the word '$ARTICLE$' if the vowels always occupy odd positions?

It is required to seat $5$ men and $4$ women in a row so that the men occupy odd places. Then the number of arrangements that are possible is

How many permutations can be formed from the letters of the word $ALGEBRA$ without changing the relative positions of the vowels and consonants?

Vedclass Test Series

Exam Paper Generator

Online Exam Module