Understanding Combinations Formulae with Example

In this class, We discuss Understanding Combinations of Formulae with Examples.

The reader should have prior knowledge of permutation formulae. Click here

Combinations mean selections.

Permutations mean arrangements.

We take an example and understand combinations formulae.

Example:

Take 26 alphabets.

How many ways do we select five alphabets from 26?

How many five-letter words are possible with 26 alphabets?

Assume we selected five alphabets: A, B, C, D, and E

These five alphabets are arranged differently, as shown in the diagram.

Similarly, we can select another five alphabets and make arrangements.

The selection is part of the arrangements.

Each time we arrange five alphabets, we have one selection.

Total number of arrangements divided by the r!, Gives selections.

N = 26 alphabets

r = 5 positions

Total arrangements = Npr = 26 p 5

= 26! / (26 – 5)!

Total selections = Npr/r!

= N! / (N-r)! r!

Number of selections = Ncr = N! / (N-r)! r!