Page 176 - DMTH202_BASIC_MATHEMATICS_II

Richa Nandra, Lovely Professional University Unit 13: Combinations

Unit 13: Combinations Notes

CONTENTS
Objectives
Introduction

13.1 Combinations
13.2 Restricted – Combinations
13.3 Binomial Coefficients

13.4 Inclusion-Exclusion Principle
13.4.1 Inclusion-Exclusion Formula
13.5 Summary
13.6 Keywords
13.7 Review Questions

13.8 Further Readings

Objectives

After studying this unit, you will be able to:

 Understand the concept of combinations
 Discuss the restricted combinations
Introduction

An arrangement of r objects, without considering order and without replication, chosen
from n different objects is known as a combination of n objects taken r at a time. Combination
signifies selection of things. The word selection is used when the order of things has no significance.
In this unit, you will understand the concept of combinations and restricted combinations.

13.1 Combinations

Definition: A combination of n objects taken r at a time is a selection of r objects from a total of
n objects (r  n), where order does not matter. The notation is usually

 n  
  
r
  
and read, “n choose r.”

The number of such combinations is indicated by

n
C 
n r
r

(n r )! !

LOVELY PROFESSIONAL UNIVERSITY 171