5 boys and 5 girls are sitting in a row rando | vedclass

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

Question

(B) Total number of ways to arrange $10$ people in a row is $n = 10!$.For boys and girls to sit alternatively,they must occupy positions like $(B, G,

Vedclass · Accepted Answer

$1/126$

Vedclass · Answer

(B) Total number of ways to arrange $10$ people in a row is $n = 10!$.For boys and girls to sit alternatively,they must occupy positions like $(B, G, B, G, B, G, B, G, B, G)$ or $(G, B, G, B, G, B, G, B, G, B)$.Case $1$: Starting with a boy,the number of arrangements is $5! 	imes 5!$.Case $2$: Starting with a girl,the number of arrangements is $5! 	imes 5!$.Total favourable ways $m = 2 	imes (5! 	imes 5!)$.Required probability $P = \frac{m}{n} = \frac{2 	imes 5! 	imes 5!}{10!}$.$P = \frac{2 	imes 120 	imes 120}{3628800} = \frac{2 	imes 120}{10 	imes 9 	imes 8 	imes 7 	imes 6} = \frac{2}{30240} 	imes 120 = \frac{2}{252} = \frac{1}{126}$.

$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is

Similar Questions

$A$ bag contains $5$ white,$7$ black,and $4$ red balls. If three balls are drawn at random from the bag,what is the probability that all three balls are white?

Two numbers are chosen at random from $\{1, 2, 3, 4, 5, 6, 7, 8\}$ at a time. The probability that the smaller of the two numbers is less than $4$ is

Two bolts,two nuts,and three needles are in a box. Two parts are chosen at random from the box. What is the probability that one is a bolt and one is a needle?

From a class of $12$ girls and $18$ boys,two students are chosen randomly. What is the probability that both of them are girls?

$3$ bulbs are drawn at random from a lot of $50$ bulbs,$5$ of which are defective. Find the probability of the event that all $3$ bulbs are non-defective (drawn without replacement).

Vedclass Test Series

Exam Paper Generator

Online Exam Module