Statistics – Combination

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected. For example, suppose we have a set of three letters: A, B, and C. we might ask how many ways we can select 2 letters from that set.

Combination is defined and given by the following function:



Where −

·        nn = the number of objects to choose from.

·        rr = the number of objects selected.


Problem Statement:

How many different groups of 10 students can a teacher select from her classroom of 15 students?


Step 1: Determine whether the question pertains to permutations or combinations. Since changing the order of the selected students would not create a new group, this is a combinations problem.

Step 2: Determine n and r

n = 15 since the teacher is choosing from 15 students.

r = 10 since the teacher is selecting 10 students.

Step 3: Apply the formula


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