The letters of the word SOCIETY are arranged | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) 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 $n(S) = 7!$.The v

Vedclass · Accepted Answer

$\frac{1}{7}$

Vedclass · Answer

(D) 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 $n(S) = 7!$.The vowels in the word are $O, I, E$ (total $3$ vowels).To find the number of arrangements where the $3$ 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.Within the group $(OIE)$,the $3$ vowels can be arranged among themselves in $3!$ ways.Thus,the number of favorable outcomes is $n(A) = 5! 	imes 3!$.The probability $P(A) = \frac{n(A)}{n(S)} = \frac{5! 	imes 3!}{7!} = \frac{5! 	imes 6}{7 	imes 6 	imes 5!} = \frac{6}{42} = \frac{1}{7}$.

The letters of the word $SOCIETY$ are arranged in a row. What is the probability that the $3$ vowels come together?

Similar Questions

Two coins are tossed. What is the probability of getting at most one head?

$A$ bag contains $2$ red,$3$ green and $2$ blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

When two dice are thrown simultaneously,what is the probability that the numbers appeared on both dice are equal?

In a class,there are $15$ boys and $10$ girls. Three students are selected at random. The probability that $1$ girl and $2$ boys are selected,is

An urn contains $25$ balls numbered $1$ to $25$. Suppose an odd number is considered a 'success'. $2$ balls are drawn from the urn with replacement. Find the probability of getting at least one success.

Vedclass Test Series

Exam Paper Generator

Online Exam Module