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WEEK FOUR
TOPIC: COMBINATION
SUB-TOPICS:
- Combination (selection).
- Conditional arrangements and selection.
- Probability problems involving arrangement and selection.
SUB-TOPIC 1
Combination (Selection)
In many situations, we make selection without regard to the order. If a committee of 4 members is to be formed from 7 members of staff of DLHS, the order in which the numbers of the given committee are selected is not important.
Combination is therefore a way of selecting items from a collection such that (unlike permutation) the order of selection does not matter.
In selecting three colours from 5 colours: (B, G, R, W, Y), BGR, BRG, GBR, RBG, RGB, are counted as 6 different arrangements (permutations), although they consist of the same 3 colours. The 6 permutations thus represent one combination. Thus, each combination of three objects yields 3! permutation.
Now, the number of the permutations of 5 colours taking 3 at a time, i.e,
The number of combinations of 5 colours taking 3 at a time, i.e,
In general,
Examples
- Out of the five science club members of a school, A, B, C, D and E, just three are to be chosen to represent the school in an exhibition. In how many ways can this be done?
- In how many ways can a committee of 3 chemistry teachers and 5 mathematics teachers be formed from 6 chemistry teachers and 10 mathematics teachers?
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