Question

7. You and 7 of your friends are watching world cup soccer and everyone decides they feel like pizza. You make an alphabetical list of all 8 names and write each one’s choice from the 10 available types of pizzas next to their name.
(a) How many possible such lists are there? (2)
(b) When the pizza restaurant receives a take-away order for 8 pizzas, how many different orders are possible? (Hint: Such an order consists only of how many of each type of pizza the caller wants.)(3)
8. Use the pigeonhole principle to show that if any n + 1 distinct numbers are chosen from the set
{1,2,3,...,2n}
then at least two of those chosen will be consecutive, i.e. you will pick a pair k,k + 1 amongst the chosen n + 1 numbers.

Answer 1