From a group of 10 men and 8 women,the number | vedclass

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

Question

(A) We need to form a committee of $8$ members from $10$ men and $8$ women such that there are at most $5$ men and at least $5$ women. Let $M$ be the

Vedclass · Accepted Answer

$8061$

Vedclass · Answer

(A) We need to form a committee of $8$ members from $10$ men and $8$ women such that there are at most $5$ men and at least $5$ women. Let $M$ be the number of men and $W$ be the number of women. Since $M+W=8$,$M \le 5$ and $W \ge 5$. The possible cases are:Case $I$: $3$ men and $5$ women. Number of ways $= {}^{10}C_3 	imes {}^{8}C_5 = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} 	imes \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 120 	imes 56 = 6720$.Case $II$: $2$ men and $6$ women. Number of ways $= {}^{10}C_2 	imes {}^{8}C_6 = \frac{10 	imes 9}{2 	imes 1} 	imes \frac{8 	imes 7}{2 	imes 1} = 45 	imes 28 = 1260$.Case $III$: $1$ man and $7$ women. Number of ways $= {}^{10}C_1 	imes {}^{8}C_7 = 10 	imes 8 = 80$.Case $IV$: $0$ men and $8$ women. Number of ways $= {}^{10}C_0 	imes {}^{8}C_8 = 1 	imes 1 = 1$.Total number of ways $= 6720 + 1260 + 80 + 1 = 8061$.

From a group of $10$ men and $8$ women,the number of ways of forming a committee of $8$ members with not more than $5$ men and not less than $5$ women is

Similar Questions

Assertion $(A)$: Rapidly changing temperatures can be measured by thermocouples. Reason $(R)$: The thermal capacity of the junction of a thermocouple is very small.

$A$ metallic ring connected to a rod oscillates freely like a pendulum. If now a magnetic field is applied in a horizontal direction so that the pendulum now swings through the field,the pendulum will

Nitrobenzene on reduction with zinc and $NH_4Cl$ gives

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the centre of mass of the system is

Sulphur is an important nutrient for optimum growth and productivity in

Vedclass Test Series

Exam Paper Generator

Online Exam Module