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

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(B) $(i)$ The word '$UNIVERSAL$' has $9$ distinct letters. The total number of arrangements of these $9$ letters is $9! = 362880$.(ii) To find the num

Vedclass · Accepted Answer

$30240$

Vedclass · Answer

(B) $(i)$ The word '$UNIVERSAL$' has $9$ distinct letters. The total number of arrangements of these $9$ letters is $9! = 362880$.(ii) To find the number of arrangements where $E, R, S$ always occur together,we treat the group $(E, R, S)$ as a single unit or block.Now,we have the letters ${U, N, I, V, A, L, (ERS)}$,which makes $7$ units in total.These $7$ units can be arranged in $7!$ ways.Within the block,the $3$ letters $E, R, S$ can be arranged among themselves in $3!$ ways.Therefore,the total number of arrangements where $E, R, S$ occur together is $7! 	imes 3! = 5040 	imes 6 = 30240$.

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

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