Math Assignment Help With Combinations

Chapter 11 Combinations


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11.1 Introduction: A combination is an un-ordered collection of distinct elements, usually of a prescribed size and taken from a given set. In other words, each of the different groups which can be formed by taking some or all the number of objects, irrespective of their arrangements is called as combinations.

For example: A salad is a combination of different fruits. It doesn't matter what is he the order of fruits. It could be “apples, pineapples and tomato” or “tomato, apple and pineapple.”

There are two types of combinations :

  • Repetition is Allowed: such as coins in your pocket (5,5,5,10,10)
  • No Repetition: such as lottery numbers (2,14,15,27,30,33)

Combination of n things taken r at a time is represented as



C(n, r) = nCr

C(n, r) is defined well when n and r are integers such that

n ≥ r

r ≥ 0

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