1. The problem statement, all variables and given/known data The eating club is hosting a make your own sundae at which the following are provided: Ice cream flavors: chocolate, cookies-n-cream, strawberry, vanilla Toppings: caramel, hot fudge, marshmellow, m & m's, nuts, strawberries a) How many sundaes are possible using one flavor of ice cream and from zero to six toppings? b) How many different combinations of flavors of three scoops of ice cream are possible if it is permissable to make all three scoops the same flavor? 2. Relevant equations n C r = n! / r! (n-r)! n P r = n! / (n-r)! 3. The attempt at a solution a) I know the answer is 256. However, I'm not sure how to get to it. I know the first part of the answer requires 4 C 1, however I'm not sure how to arrive at 4 * 64. b) Answer is 20. They are asking for something equivalent to 4 C 3, which would be 4. However, I am guessing since it is possible to use the same flavor, the answer is multiplied 4 times, plus the 4 sets of the same flavors (i.e. [(4 C 3) * 4] + 4).