The probability of forming a 12-person commit | vedclass

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

Question

(A) Total number of ways to select $12$ persons from $16$ $(4+2+10)$ is $^{16}C_{12} = ^{16}C_4 = \frac{16 	imes 15 	imes 14 	imes 13}{4 	imes 3 \

Vedclass · Accepted Answer

$\frac{129}{182}$

Vedclass · Answer

(A) Total number of ways to select $12$ persons from $16$ $(4+2+10)$ is $^{16}C_{12} = ^{16}C_4 = \frac{16 	imes 15 	imes 14 	imes 13}{4 	imes 3 	imes 2 	imes 1} = 1820$. We need at least $3$ engineers and at least $1$ doctor. The possible cases are: $1)$ $3$ Engineers,$1$ Doctor,$8$ Professors: $^4C_3 	imes ^2C_1 	imes ^{10}C_8 = 4 	imes 2 	imes 45 = 360$. $2)$ $3$ Engineers,$2$ Doctors,$7$ Professors: $^4C_3 	imes ^2C_2 	imes ^{10}C_7 = 4 	imes 1 	imes 120 = 480$. $3)$ $4$ Engineers,$1$ Doctor,$7$ Professors: $^4C_4 	imes ^2C_1 	imes ^{10}C_7 = 1 	imes 2 	imes 120 = 240$. $4)$ $4$ Engineers,$2$ Doctors,$6$ Professors: $^4C_4 	imes ^2C_2 	imes ^{10}C_6 = 1 	imes 1 	imes 210 = 210$. Total favorable ways = $360 + 480 + 240 + 210 = 1290$. Required probability = $\frac{1290}{1820} = \frac{129}{182}$.

The probability of forming a $12$-person committee from $4$ engineers,$2$ doctors,and $10$ professors containing at least $3$ engineers and at least $1$ doctor is:

Similar Questions

From a group of $50$ students,two sections comprising of $20$ and $30$ students are formed. If $Ram$ and $Rahim$ are two particular students among the $50$ students,then the probability that they both belong to the same section is

Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains at least $3$ Kings.

From a pack of $52$ cards,$3$ cards are drawn at random. Then,the probability that one is an ace,one is a queen,and one is a jack is

If three integers are selected at random from the first $20$ integers,what is the probability that their product is even?

If $4$-digit numbers greater than $5,000$ are randomly formed from the digits $0, 1, 3, 5,$ and $7$,what is the probability of forming a number divisible by $5$ when the digits are repeated?

Vedclass Test Series

Exam Paper Generator

Online Exam Module