(B) Total number of ways to select $5$ members from $10$ people ($6$ men + $4$ women) is ${}^{10}C_5 = \frac{10 \times 9 \times 8 \times 7 \times 6}{5

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

(B) Total number of ways to select $5$ members from $10$ people ($6$ men + $4$ women) is ${}^{10}C_5 = \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1} = 252$.The number of ways to select a committee with no women (i.e.,all $5$ members are men) is ${}^6C_5 = 6$.The number of ways to select at least one woman is (Total ways) - (Ways with no women) = $252 - 6 = 246$.The required probability is $P = \frac{246}{252} = \frac{41}{42}$.

Class 11 Mathematics Probability Advanced Use of permutations and combinations in probability

Medium

$A$ committee of $5$ members is to be formed from $6$ men and $4$ women. What is the probability that the committee contains at least one woman?

A
$\frac{1}{42}$
B
$\frac{41}{42}$
C
$\frac{2}{63}$
D
$\frac{1}{7}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Probability

Subtopic

Advanced Use of permutations and combinations in probability

If a $5$-digit number is chosen at random,what is the probability that all digits are distinct,odd digits occupy odd places,and even digits occupy even places?

Medium

View Solution

Seven balls are drawn simultaneously from a bag containing $5$ white and $6$ green balls. The probability of drawing $3$ white and $4$ green balls is:

DifficultTS EAMCET 2006

View Solution

$A$ bag contains $6$ blue and $6$ green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is:

DifficultJEE MAIN 2026

View Solution

From a group of $7$ men and $4$ ladies,a committee of $6$ persons is formed. What is the probability that the committee contains exactly $2$ ladies?

Easy

View Solution

If $4$ letters are selected at random from the letters of the word $PROBABILITY$, then the probability of getting a combination of letters in which at least one letter is repeated is

MediumTS EAMCET 2024

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ committee of $5$ members is to be formed from $6$ men and $4$ women. What is the probability that the committee contains at least one woman?

Similar Questions

If a $5$-digit number is chosen at random,what is the probability that all digits are distinct,odd digits occupy odd places,and even digits occupy even places?

Seven balls are drawn simultaneously from a bag containing $5$ white and $6$ green balls. The probability of drawing $3$ white and $4$ green balls is:

$A$ bag contains $6$ blue and $6$ green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is:

From a group of $7$ men and $4$ ladies,a committee of $6$ persons is formed. What is the probability that the committee contains exactly $2$ ladies?

If $4$ letters are selected at random from the letters of the word $PROBABILITY$, then the probability of getting a combination of letters in which at least one letter is repeated is

Vedclass Test Series

Exam Paper Generator

Online Exam Module