In how many different ways can the letters of | vedclass

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(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?

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