In how many ways can the letters of the word | vedclass

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(C) The word '$UNIVERSAL$' contains $9$ distinct letters: $U, N, I, V, E, R, S, A, L$.Since $E, R, S$ must always be together,we treat the group $(ERS

Vedclass · Accepted Answer

$30240$

Vedclass · Answer

(C) The word '$UNIVERSAL$' contains $9$ distinct letters: $U, N, I, V, E, R, S, A, L$.Since $E, R, S$ must always be together,we treat the group $(ERS)$ as a single unit.Now,the letters to be arranged are ${U, N, I, V, A, L, (ERS)}$.This gives us a total of $7$ units to arrange,which can be done in $7!$ ways.Within the group $(ERS)$,the $3$ letters can be arranged among themselves in $3!$ ways.Therefore,the total number of arrangements is $7! 	imes 3!$.Calculating the values: $7! = 5040$ and $3! = 6$.Total arrangements $= 5040 	imes 6 = 30240$.

In how many ways can the letters of the word '$UNIVERSAL$' be arranged when $E, R, S$ are always together?

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