1. How many bitstrings are there that are at least 3 bits and at most 7 bits long? (Answer: 248)
2. An ice cream shop has 2 different flavors of ice cream (vanilla and chocolate), 3 different
sauces (chocolate, caramel, and strawberry), and 4 additional toppings (nuts, coconut, cherries,
and banana). If a sundae consists of one scoop of ice cream, one sauce, and one additional
topping, how many sundaes are possible? (Answer: 24)
3. How many integers between 1000 and 2000 (inclusive) are divisible by 5 or 7 or 11? (Answer:
378)
4. If you flip a fair coin 10 times, how many of the possible outcomes start with a string of 3
Heads or end with a string of 3 Tails? (i.e. start with \"HHH\" or end with \"TTT\")? (Answer: 240)
5. What is the minimum number of people in a group that would guarantee that at least 10 were
born on the same day of the week? (Answer: 64)
6. A variable in some programming language can be either a single digit (0 to 9) or a boolean (T
or F). How many options are there for the value of this variable? (Answer: 12)