A bag contains two red marbles, two green ones, one lavender one, three yellows, and two orange marbles.  How many possible sets of four marbles are there?

In a​ bag, there are 6 purple and 12 green marbles. If you reach in and randomly choose 5 ​marbles, without​ replacement, in how many ways can you choose exactly one​ purple?

An ice cream store stocks 30 different flavors and offers rainbow banana boat split that contains 3 scoops of ice cream each of a different flavor. On a banana boat they put one scoop of ice cream on the left one scoop in the middle and one scoop on the right of the banana boat. How many different rainbow splits can the store advertise?

A birthday cake is to have two layers of cake separated by a layer of icing, with another layer of icing on top. There are 3 kinds of cake the chef knows how to make, and she may use either two different kinds or the same one twice for the two cake layers. The chef knows recipes for 4 different icings, and she will use two different recipes, one for each icing layer, in this cake. How many different cakes could the chef make? Note that the order of the layers matters, e.g. chocolate over strawberry is different from strawberry over chocolate.

A salesperson wants to display five bracelets in the store window. There are a total of nine different bracelets in stock. How many combinations of five bracelets are possible?

Suppose you have a choice of ten TV sets that can be matched with any of six DVR players and eight DVD players. How many different TV/DVR/DVD systems can you assemble?

A dish contains 2 yellow, 4 red, 5 purple, 2 green, and 3 orange candies.  How many sets of 7 candies include at least 3 purple ones?

How many different baseball bating line ups are possible if the coach wants to put one of the three best batters in the third position and the pitcher in the fifth position?

If there are 5 logs in a pile of 30 that have sap on them, how many logs will have sap out of 360?

A track coach needs to select 2 students from each grade level to cre- ate a board of representatives. If there are 10 seniors, 10 juniors, 14, sophomores, and 15 freshmen, how many possible different boards can be chosen? A 19,348,875 B 309,582,000 450,978,066 D 18,183,435,621,120