A committee of 12 members is to be formed fro | vedclass

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

Question

(B) committee of $12$ members is to be formed such that women are in majority. The total number of women is $9$ and men is $8$.Case $I$: $9$ women and

Vedclass · Accepted Answer

$2702$

Vedclass · Answer

(B) committee of $12$ members is to be formed such that women are in majority. The total number of women is $9$ and men is $8$.Case $I$: $9$ women and $3$ men$	ext{Number of ways} = {^9C_9} 	imes {^8C_3} = 1 	imes \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$Case $II$: $8$ women and $4$ men$	ext{Number of ways} = {^9C_8} 	imes {^8C_4} = 9 	imes \frac{8 	imes 7 	imes 6 	imes 5}{4 	imes 3 	imes 2 	imes 1} = 9 	imes 70 = 630$Case $III$: $7$ women and $5$ men$	ext{Number of ways} = {^9C_7} 	imes {^8C_5} = \frac{9 	imes 8}{2 	imes 1} 	imes \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 36 	imes 56 = 2016$$	ext{Total number of ways} = 56 + 630 + 2016 = 2702$

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is

Similar Questions

On a temperature scale $Y$,water freezes at $-160^{\circ} Y$ and boils at $-50^{\circ} Y$. On this $Y$ scale,a temperature of $340 \ K$ is (in $^{\circ} Y$)

Which one of the following pairs of reactants does not form oxygen when they react with each other?

$A$ sound absorber attenuates the sound level by $20\, dB$. The intensity decreases by a factor of:

If the slope of one of the lines given by $ax^2+2hxy+by^2=0$ is two times the other,then:

Which of the following is known as the $Christmas$ tree?

Vedclass Test Series

Exam Paper Generator

Online Exam Module