Example: Combinations and Permutations
Use the combin and permut functions to count subsets of items. The order of the items is significant in permutations but not in combinations.
1. Set the number of items and the number of items in each subset:
2. Apply function combin to calculate the number of combinations:
When dealing with four items, there are four ways to group one item at a time, six ways to group two items at a time, four ways to group three items at a time, and one way to group four items at a time.
3. Assume we have letters A, B, C, and D. List the four combinations of one letter per set:
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A, B, C, D
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4. List the six combinations of two letters per set:
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AB, AC, AD, BC, BD, CD
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Sets BA, CA, DA, CB, DB, DC contain the same letters as AB, AC, etc, and thus are not counted as different combinations.
5. Apply function permut to calculate the number of permutations:
6. List the 12 permutations of two letters per set:
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AB, AC, AD, BC, BD, CD
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BA, CA, DA, CB, DB, DC
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Sets AB and BA are treated as different permutations of A and B.
7. List the 24 permutations of three letters per set:
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ABC, ACB, ABD, ADB, ACD, ADC
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BAC, BCA, BAD, BDA, BCD, BDC
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CAB, CBA, CAD, CDA, CBD, CDB
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DAB, DBA, DBC, DCB, DAC, DCA
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