There are 7 men and 8 women in a club. A comm | vedclass

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

Question

(A) Total number of people in the club $= 7 + 8 = 15$.Total number of ways to select $6$ persons out of $15$ is given by ${}^{15}C_6$.${}^{15}C_6 = \f

Vedclass · Accepted Answer

$4998$

Vedclass · Answer

(A) Total number of people in the club $= 7 + 8 = 15$.Total number of ways to select $6$ persons out of $15$ is given by ${}^{15}C_6$.${}^{15}C_6 = \frac{15 	imes 14 	imes 13 	imes 12 	imes 11 	imes 10}{6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1} = 5005$.To find the number of ways such that at least one woman is selected,we subtract the number of ways where no woman is selected (i.e.,all $6$ are men) from the total number of ways.Number of ways to select $6$ men out of $7$ is ${}^{7}C_6$.${}^{7}C_6 = {}^{7}C_1 = 7$.Required number of ways $= {}^{15}C_6 - {}^{7}C_6 = 5005 - 7 = 4998$.

There are $7$ men and $8$ women in a club. $A$ committee is formed using these persons. What will be the number of ways to select $6$ persons such that at least one is a woman?

Similar Questions

In how many ways can a committee,consisting of $5$ men and $6$ women,be formed from $8$ men and $10$ women?

$A$ box contains $2$ white balls,$3$ black balls and $4$ red balls. In how many ways can $3$ balls be drawn from the box,if at least one black ball is to be included in the draw?

$\sum_{0 \le i < j \le n} i \binom{n}{j}$ is equal to

There are $6$ members to be selected for a group to be sent abroad from a total of $12$ members. In how many ways can the selection be made such that a particular member is always excluded?

The number of positive integral solutions of $a \cdot b \cdot c = 30$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module