Q. 123

# A team consists of 6 boys and 4 girls, and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy, and a girl plays against a girl?

Given: Singles matches are to be played, either a boy plays against a boy, and a girl plays against a girl.

A number of ways to select a boy from team 1 is 6C1. Similarly, Number of ways to select a boy from team 2 is 5C1

Hence number of singles matches between boys is 6C1 × 5C1 = 6 × 5 = 30

A number of ways to select a girl from team 1 is 4C1. Similarly, Number of ways to select a girl from team 2 is 3C1

Hence number of singles matches between girls is 3C1 × 4C1 = 4 × 3 = 12

The total number of matches = 30 + 12 = 42.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Circular permutations61 mins
Challenging Quiz on P&C | Test Yourself55 mins
Permutations & Combinations | Analyze your learningFREE Class
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Understand Permutations like never before60 mins
Lecture on Combinations49 mins
Interactive Quiz on Division and distribution of objects17 mins
Interactive Quiz on Combinations-0253 mins
Interactive Quiz on Combinations50 mins
Division and distribution of objects58 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
view all courses