Quantitative Finance
# Probability Theory

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?

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.