A committee of 12 is to be formed from 9 wome | vedclass

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

Question

(D) Total committee size is $12$. We have $9$ women and $8$ men.
Condition: At least $5$ women must be included.
Possible cases for (Women,Men) are:

Vedclass · Accepted Answer

$2702, 1008$

Vedclass · Answer

(D) Total committee size is $12$. We have $9$ women and $8$ men.
Condition: At least $5$ women must be included.
Possible cases for (Women,Men) are: $(5, 7), (6, 6), (7, 5), (8, 4), (9, 3)$.
Number of ways = $^9C_5 	imes ^8C_7 + ^9C_6 	imes ^8C_6 + ^9C_7 	imes ^8C_5 + ^9C_8 	imes ^8C_4 + ^9C_9 	imes ^8C_3$
$= (126 	imes 8) + (84 	imes 28) + (36 	imes 56) + (9 	imes 70) + (1 	imes 56)$
$= 1008 + 2352 + 2016 + 630 + 56 = 6062$.
$(i)$ Women are in majority if women count $> 6$ (i.e.,$7, 8, 9$ women):
$= ^9C_7 	imes ^8C_5 + ^9C_8 	imes ^8C_4 + ^9C_9 	imes ^8C_3 = 2016 + 630 + 56 = 2702$.
(ii) Men are in majority if men count $> 6$ (i.e.,$7$ men):
$= ^9C_5 	imes ^8C_7 = 126 	imes 8 = 1008$.

$A$ committee of $12$ is to be formed from $9$ women and $8$ men in which at least $5$ women have to be included in a committee. Then the number of committees in which the women are in majority and men are in majority are respectively

Similar Questions

Everybody in a room shakes hands with everybody else. The total number of handshakes is $66$. The total number of persons in the room is:

Find the number of ways of selecting $9$ balls from $6$ red balls,$5$ white balls,and $5$ blue balls,if each selection consists of $3$ balls of each colour.

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

If the four-letter words (need not be meaningful) are to be formed using the letters from the word "$MEDITERRANEAN$" such that the first letter is $R$ and the fourth letter is $E,$ then the total number of all such words is

$A$ question paper is divided into two parts $A$ and $B$,and each part contains $5$ questions. The number of ways in which a candidate can answer $6$ questions by selecting at least two questions from each part is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module