Q. 205.0( 1 Vote )

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of this committee would consist of 1 man and 2 women?

Answer :

Given that we need to select 3 persons out of 2 men and 3 women,


Let us assume the no. of ways of selecting be N,


N = selecting 3 persons out of total 5 persons


N = 5C3


We know that


And also n! = (n)(n – 1)(n – 2)…………2.1





N = 10 ways


The no. of ways of selecting 3 persons out of 2 men and 3 women is 10.


(ii) It is told that 1 man and 2 women should be selected out of 2 men and 3 women.


Let us assume the no. of ways of selection be N1,


N1 = (selecting one man out of 2 men) × (selecting 2 women out of 3 women)


N1 = (2C1) × (3C2)


We know that


And also n! = (n)(n – 1)(n – 2)…………2.1





N1 = 6 ways


The no. of ways of selecting 1 man and 2 women is 6.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Permutations & Combinations | Analyze your learningPermutations & Combinations | Analyze your learningPermutations & Combinations | Analyze your learningFREE Class
Challenging Quiz on P&C | Test YourselfChallenging Quiz on P&C | Test YourselfChallenging Quiz on P&C | Test Yourself55 mins
Lecture on CombinationsLecture on CombinationsLecture on Combinations49 mins
Interactive Quiz on Division and distribution of objectsInteractive Quiz on Division and distribution of objectsInteractive Quiz on Division and distribution of objects17 mins
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationCheck Your progress Part 2| Interactive Quiz: Permutation & CombinationCheck Your progress Part 2| Interactive Quiz: Permutation & Combination54 mins
Understand Permutations like never beforeUnderstand Permutations like never beforeUnderstand Permutations like never before60 mins
Combinations - BOX & GAP MethodCombinations - BOX & GAP MethodCombinations - BOX & GAP Method38 mins
Interactive Quiz on CombinationsInteractive Quiz on CombinationsInteractive Quiz on Combinations50 mins
Division and distribution of objectsDivision and distribution of objectsDivision and distribution of objects58 mins
Interactive Quiz on Combinations-02Interactive Quiz on Combinations-02Interactive Quiz on Combinations-0253 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :