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# Formula to yield how many decision makers premised on how many employees and combinations thereof.

Thu 10 Oct, 2013 06:47 am
Please tell me the algorithm I can use to construct a simple mathematical formula to give me the total number of combinations available every time I add or subtract one person from the group.

For instance, in a one-man operation (Mr. "A"), all decisions are made for his organization by that one person. If he adds an assistant (Mr. "B"), then the combination of possible decision makers is 3, i.e., all decision made by Mr. "A"; or all decisions made by Mr. B; or all decisions made by a combination of Mr. A and Mr. B. Hence the total number of possibilities is three (3).

If one additional person (Mr, "C") joins the group, the exponential number of decision making combinations jumps to 6, i.e., all decisions made by person "A"; all decisions made by person "B"; all decisions made by person "C"; all decisions made by a combination of A+B; A+B+C; A and B; A and C; C and B; B+A , for a total of 8 combinations.

Using this reasoning, if we add person "D" to the group, the expotential number of decision-makers jumps to as follows:

INDIVIDUALS COMBINATION(S)

A alone 1
B alone 2
C alone 3
A+B 4
A+C 5
B+C 6

I am looking for a formula that would instantly give me the correct answer to the hypothetical question: "I have "X" equally ranked employees. How many combinations of decision makers do I have?

That formula plus any suggestions as to how I could better express this problem would b greatly appreciated.

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