Count different orders
An arrangement records what comes first and second. If you use A and B once each, AB and BA are two different arrangements.
Both use the same symbols; their order is different. Repeats are not allowed here, so AA and BB are excluded.
Count the same group once
Now ask only which two symbols were chosen. AB and BA both choose A and B. They form one group because order does not matter.
If you start by counting orders, divide by the two orders of each pair: 2 ÷ 2 = 1 group. Swapping the symbols does not create another group.
Choose two from three
Choose two distinct symbols from C, D and E. Order does not matter.
Use each symbol at most once. Count a group only once, even when its symbols can be written in reverse order.
Try it
How many groups of two can you choose from C, D and E, without repeats or regard to order?
- 3
- 6
Show the answer
3
Correct. The groups are CD, CE and DE: 3 groups. Reversing their order does not create new groups.
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Practice Counting combinations