In how many different ways can the letters of | vedclass

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

Question

(A) The word '$JUDGE$' consists of $5$ distinct letters: $J, U, D, G, E$.The vowels in the word are $U$ and $E$. The consonants are $J, D, G$.To ensur

Vedclass · Accepted Answer

$48$

Vedclass · Answer

(A) The word '$JUDGE$' consists of $5$ distinct letters: $J, U, D, G, E$.The vowels in the word are $U$ and $E$. The consonants are $J, D, G$.To ensure the vowels always come together,we treat the group $(UE)$ as a single unit.Now,we have $4$ units to arrange: ${J, D, G, (UE)}$.These $4$ units can be arranged in $4!$ ways,which is $4 	imes 3 	imes 2 	imes 1 = 24$ ways.Within the group $(UE)$,the $2$ vowels can be arranged among themselves in $2!$ ways,which is $2 	imes 1 = 2$ ways.Therefore,the total number of arrangements is $24 	imes 2 = 48$ ways.

In how many different ways can the letters of the word '$JUDGE$' be arranged in such a way that the vowels always come together?

Similar Questions

The number of integers greater than a million that can be formed using the digits $2, 3, 0, 3, 4, 2, 3$ is:

How many $3$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5, 6$ when
$(i)$ repetition of digits is not allowed
(ii) repetition of digits is allowed?

In how many ways can $3$ letters be posted in $4$ letter-boxes,if all the letters are not posted in the same letter-box?

Out of $5$ apples,$10$ mangoes,and $15$ oranges,$15$ fruits are to be distributed between two persons. Find the total number of ways of distribution.

The value of ${2^n} \{ 1 \cdot 3 \cdot 5 \cdots (2n - 3) \cdot (2n - 1) \}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module