The letters of the word SOCIETY are placed in | vedclass

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(C) The word $SOCIETY$ contains $7$ distinct letters: $S, O, C, I, E, T, Y$. The total number of ways to arrange these $7$ letters is $7! = 5040$.Ther

Vedclass · Accepted Answer

$\frac{1}{7}$

Vedclass · Answer

(C) The word $SOCIETY$ contains $7$ distinct letters: $S, O, C, I, E, T, Y$. The total number of ways to arrange these $7$ letters is $7! = 5040$.There are $3$ vowels in the word: $O, I, E$. To find the number of arrangements where these $3$ vowels come together,we treat the group $(O, I, E)$ as a single unit.Now,we have $5$ units to arrange: $(OIE), S, C, T, Y$. These $5$ units can be arranged in $5!$ ways.The $3$ vowels within the group can be arranged among themselves in $3!$ ways.Therefore,the total number of favorable arrangements $= 5! 	imes 3! = 120 	imes 6 = 720$.The required probability $= \frac{	ext{Favorable arrangements}}{	ext{Total arrangements}} = \frac{5! 	imes 3!}{7!} = \frac{120 	imes 6}{5040} = \frac{720}{5040} = \frac{1}{7}$.

The letters of the word $SOCIETY$ are placed in a row. What is the probability that the three vowels come together?

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