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# Rule of Sum and Rule of Product

Seek simple and succinct solutions in these systems by sussing-out the significant symmetries.

# Rule of Sum and Rule of Product Problem Solving

Aleasha has a standard 6-sided die and a coin. If she chooses one of them and then rolls or flips it, how many different results can she get?

There are $$8$$ cards with number $$10$$ on them, $$5$$ cards with number $$100$$ on them and $$2$$ cards with number $$500$$ on them. How many distinct sums are possible using from 1 to all of the $$15$$ cards?

Paddy flips a fair coin $$6$$ times, and writes down each result in order. What is the total number of possible outcomes?

Note: The outcome $$THHH$$ is different from the outcome $$HHHT$$.

How many ways are there to color the above regions with 4 different colors, if adjacent regions should have different colors?

Note: You need not use all four colors but each region must be colored by any one of them.

How many odd 3-digit numbers are there, whose digits are distinct integers from the set $$\{0, 1, 2, 3, 4, 5, 6, 7 \}$$.

This problem is posed by Gabriel M.

Details and assumptions

The number $$12=012$$ is a 2-digit number, not a 3-digit number.

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