In how many different ways can the letters of | vedclass

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(B) The word '$OPTICAL$' contains $7$ distinct letters: $O, P, T, I, C, A, L$.The vowels in the word are $O, I, A$. Since they must always come togeth

Vedclass · Accepted Answer

$720$

Vedclass · Answer

(B) The word '$OPTICAL$' contains $7$ distinct letters: $O, P, T, I, C, A, L$.The vowels in the word are $O, I, A$. Since they must always come together,we treat them as a single unit or block: $(OIA)$.Now,the remaining letters are $P, T, C, L$.Including the block $(OIA)$,we have $4 + 1 = 5$ units to arrange.These $5$ units can be arranged in $5!$ ways.Within the block $(OIA)$,the $3$ vowels can be arranged among themselves in $3!$ ways.Therefore,the total number of arrangements $= 5! 	imes 3! = 120 	imes 6 = 720$ ways.

In how many different ways can the letters of the word '$OPTICAL$' be arranged so that the vowels always come together?

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