A committee consists of 9 experts taken from | vedclass

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

Question

(D) Total number of experts $= 2 + 3 + 4 = 9$.We need to select $3$ experts out of $9$ to resign. The total number of ways to choose $3$ experts is gi

Vedclass · Accepted Answer

$\frac{2}{7}$

Vedclass · Answer

(D) Total number of experts $= 2 + 3 + 4 = 9$.We need to select $3$ experts out of $9$ to resign. The total number of ways to choose $3$ experts is given by ${}^9C_3 = \frac{9 	imes 8 	imes 7}{3 	imes 2 	imes 1} = 84$.We want the probability that the $3$ experts belong to different institutions. This means we must select $1$ expert from institution $A$,$1$ from $B$,and $1$ from $C$.The number of ways to select $1$ expert from each is ${}^2C_1 	imes {}^3C_1 	imes {}^4C_1 = 2 	imes 3 	imes 4 = 24$.The required probability is $\frac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}} = \frac{24}{84}$.Simplifying the fraction,$\frac{24}{84} = \frac{2}{7}$.

$A$ committee consists of $9$ experts taken from three institutions $A, B$ and $C$,of which $2$ are from $A, 3$ from $B$ and $4$ from $C$. If three experts resign,then the probability that they belong to different institutions is

Similar Questions

$A$ man and his wife appear for an interview for two posts. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's selection is $\frac{1}{5}$. What is the probability that only one of them will be selected?

$4$ coins are tossed once. Find the probability of getting exactly $3$ tails.

An integer is chosen at random from the first $200$ natural numbers. What is the probability that the integer chosen is divisible by $6$ or $8$?

Out of $40$ consecutive natural numbers,two are chosen at random. The probability that the sum of the numbers is odd is:

If $P(A) = \frac{2}{3}$,$P(B) = \frac{4}{9}$ and $P(A \cap B) = \frac{14}{45}$,then find $P(A \cup B)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module