Add the numbers across each row of Pascal’s triangle. Do the results look familiar?
Example Finding All Subsets of a Set Systematically Find all subsets of the set {1, 2, 3, 4}.
We can organize this problem by considering subsets according to their size, going from 0 to 4. This method is illustrated in the following table.
Size of Subset | Subsets of This Size
| Number of Subsets of This Size |
0 | ∅ | 1 |
1 | {1}, {2}, {3}, {4} | 4 |
2 | {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4} | 6 |
3 | {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4} | 4 |
4 | {1, 2, 3, 4} | 1 |
5 |
| Total = 16 |
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