How many words can be formed using the letter | vedclass

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

Question

(B) The word $BHARAT$ contains $6$ letters,where the letter $A$ is repeated twice.Total number of arrangements $= \frac{6!}{2!} = \frac{720}{2} = 360$

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(B) The word $BHARAT$ contains $6$ letters,where the letter $A$ is repeated twice.Total number of arrangements $= \frac{6!}{2!} = \frac{720}{2} = 360$.To find the number of words where $B$ and $H$ are together,we treat $(BH)$ as a single unit.Now,we have $5$ units: $(BH), A, R, A, T$.The number of arrangements of these $5$ units,where $A$ is repeated twice,is $\frac{5!}{2!} = \frac{120}{2} = 60$.Since $B$ and $H$ can be arranged among themselves in $2! = 2$ ways,the total number of arrangements where $B$ and $H$ are together is $60 	imes 2 = 120$.Therefore,the number of words where $B$ and $H$ are never together $= 	ext{Total arrangements} - 	ext{Arrangements where } B 	ext{ and } H 	ext{ are together}$.$= 360 - 120 = 240$.

How many words can be formed using the letters of the word $BHARAT$ such that $B$ and $H$ never come together?

Similar Questions

If all the seven letters of the word $LEADING$ are permuted in all possible ways and the words thus formed are arranged as in the dictionary order,then the word in $2017^{\text{th}}$ place is

Find the number of permutations of the letters of the word $ALLAHABAD$.

In how many ways can the letters of the word $PERMUTATIONS$ be arranged if there are always $4$ letters between $P$ and $S$?

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?

$A$ number lock has $3$ rings and each ring has $8$ digits. The total number of different ways in which the $3$ rings can be rotated is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module