A group of elements is said to be ordered if the order in which these elements are drawn is of relevance, otherwise it is called unordered. For example,
Suppose there are three balls of different colours, black, grey, and white, are drawn. Now there are two options:
The first option is to take into account the order in which the balls are drawn. In such a situation, multiple possible sets of balls can be possible, such as (black, grey, and white) (white, black, and grey) and many others. In this type of construction, we can have different sets, and each set can be treated differently, and such set is called an ordered set.
In the second option, we do not take into account the order in which the balls are drawn. In such a situation, the two possible sets of balls such as (black, grey, and white) and (white, black, and grey) are the same sets and constitute an unordered set of balls.
Ordered samples
- The first three places in a 100m race are determined by the order in which the athletes arrive at the finishing line. Suppose if 8 athletes are competing with each other, the number of possible results for the three places is of interest.
- In a lottery with two prizes, the first drawn lottery ticket gets the first prize, and the second lottery ticket gets the second prize.
Unordered samples
- The selected members for a football team. The order in which the selected names are announced is irrelevant.
- Fishing 20 fish from a lake.
- A bunch of 10 flowers made from 21 flowers of 4 different colours.
Reference
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