Probability

# Rule of Sum and Rule of Product Problem Solving

Aleasha has a standard 6-sided die and a coin.

How many different results can she get in rolling the die or flipping the coin?

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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