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S= {A,B,B,C,C,C,D,D,D,D,E,E,E,E,E}.

If I choose n element from S, how many possible combination (unordered) and permutation (ordered) are possible (without using decision tree or counting)? What is your thought process and the concept/trick used?

Example for n=2, There are 14 possible combination (unordered) subset. (if I didn't miss something..) {A,B},{A,C},{A,D},{A,E},{B,B},{B,C},{B,D},{B,E},{C,C},{C,D},{C,E},{D,D},{D,E},{E,E} and there are 24 possible permutation.

if general n isn't feasible. how about n=7 and n=15 (all) ?

N. F. Taussig
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Agustinus Law
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1 Answers1

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Hint regarding the number of combinations: write the generating function. It is very well explained here: Combinations of colored balls.

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Jens
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