Combinations

Example 6: How many lines can you draw using 3 non collinear (not in a single line) points A, B and C on a plane?

Solution:

You need two points to draw a line. The order is not important. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we proceed as we did with permuatations, we get the following pairs of points to draw lines.

AB , AC

BA , BC

CA , CB

There is a problem: line AB is the same as line BA, same for lines AC and CA and BC and CB.

The lines are: AB, BC and AC ; 3 lines only.

So in fact we can draw 3 lines and not 6 and that's because in this problem the order of the points A, B and C is not important.

This is a combination problem: combining 2 items out of 3 and is written as follows:

n C r = n! / [ (n - r)! r! ]



The number of combinations is equal to the number of permuations divided by r! to eliminates those counted more than once because the order is not important

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