10. Darnell decides to roll two 15-sided numbered polyhedrons. (a) How many total outcomes are there? (b) How many ways can Darnell get a sum of 12?

You break your piggy-bank to discover lots of pennies and nickels. You start arranging these in rows of 6 coins. a. You find yourself making rows containing an equal number of pennies and nickels. For fun, you decide to lay out every possible such row. How many coins will you need? b. How many coins would you need to make all possible rows of 6 coins (not necessarily with equal number of pennies and nickels)?

1. Dr. Orchid has 9 paintings she wants to hang side by side on her wall. (a) In how many ways can she arrange all 9 paintings? Show your work. (b) If she only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? Show your work.

Three hungry pirates, Ahab, Bluebeard, and Hook, were stranded on a desert island. They came upon a treasure chest, which they immediately opened. To their joy, they found it to be full of pretzels! Immediately they each ate 10, then they decided they should save the rest for later. That night, after the others had fallen asleep, Ahab crept to the treasure chest and opened it. He separated the pretzels into 3 equal piles. There was 1 extra pretzel, which he gave to a passing monkey. Then he stole one of the 3 equal piles of pretzels, put the rest back into the chest, and went back to camp. A short time later Bluebeard sneaked over to the chest. He separated the pretzels into four equal piles (he wasn’t quite as greedy as Ahab). There were 2 extra pretzels, which he gave to a passing monkey. He then stole one of the four piles and put the rest back into the chest. Still later Hook went to the chest and separated the pretzels into five equal piles. There were 3 left over, which he gave…