Combination Problem: possible combinations for some cartoon drawings

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Mr Thorboto

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My son is trying to figure out the number of possible combinations for some cartoon drawings he is working on. I cannot remember the formula to use. It seems to me that the basic permutations and combination formulas don't work. There are 8 different categories to. In each category there are 5 items to choose from (e.g. The head category has round, triangle, square, oval, and rectangle). If he has to use one from each category, how many possible combinations are there? To make it a little more complex, what if the categories have different amounts (e.g., heads have 5 options and eyes have 6 options).

Thanks,
Clint
 
Mr Thorboto said:
My son is trying to figure out the number of possible combinations for some cartoon drawings he is working on. I cannot remember the formula to use. It seems to me that the basic permutations and combination formulas don't work. There are 8 different categories to. In each category there are 5 items to choose from (e.g. The head category has round, triangle, square, oval, and rectangle). If he has to use one from each category, how many possible combinations are there? To make it a little more complex, what if the categories have different amounts (e.g., heads have 5 options and eyes have 6 options).

Thanks,
Clint
Click to expand...

All you need here is the multiplication principle. For instance, if you have 7 choices for head, and then 3 choices for eyes, there are 7*3 = 21 ways to choose both head and eyes.

The formulas for permutations and combinations are derived from this more basic idea.
 
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