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WEEK THREE
TOPIC: PERMUTATIONS
SUB-TOPICS:
- Permutation (arrangement).
- Cyclic permutation.
- Arrangement of identical objects.
- Arrangement in which repetitions are allowed.
SUB-TOPIC 1
Permutation (Arrangement)
Suppose we are interested in the different arrangement of two people in a line. If these two people are labelled a and b then the problem is the same as finding the different arrangement of the letters a and b.
The number of arrangements will be two i.e. ab and ba.
Suppose there are three people in the line labelled a, b, and c. finding the different arrangements will be the same as finding the arrangements of the letters a, b and c.
| b |
From the above, we see there are six different arrangements.
We can get the number of different arrangements of an arbitrary n terms.
| N | No. of different arrangements | Formula |
| 1 | 1 | 1 |
| 2 | 2 | 2 x 1 |
| 3 | 6 | 3 x 2 x 1 |
| 4 | 24 | 4 x 3 x 2 x 1 |
| 5 | 120 | 5 x 4 x 3 x 2 x 1 |
Based on the above pattern, the number of different arrangement of n objects will be:
This product can be written as n for short. n is read n-factorial.
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