Does anybody know how many different combinations there are for the numbers 1, 2, 3, 4, 5 and 6?
That depends on how many of those six numbers you take.
If you only take one number, there are six combinations: {1}, {2}, {3}, {4}, {5}, and {6}.
If you take two numbers, there are fifteen combinations: {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {2,3}, {2,4}, {2,5}, {2,6}, {3,4}, {3,5}, {3,6}, {4,5}, {4,6}, and {5,6}.
If you take three numbers, there are twenty combinations.
If you take four numbers, there are fifteen combinations.
If you take five numbers, there are six combinations.
If you take all six numbers, there is only one combination: {1,2,3,4,5,6}.
In general, if you take 'm' objects out of a set of 'n' objects, the number of combinations is given by n!/[(m!)(n-m)!] where '!' is the factorial operator.
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