In how many ways can you sit 8 people on a round table if Grace and Joey, who are members of the group want to sit together all the tim

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 poker hand consists of five cards from a deck of 52.  Order does not matter.  In how many ways can the hand consist of 3 hearts and 2 spades?

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?

The security department at six employees. Four of them won’t have to work on Thanksgiving day. How many different ways can the supervisors elect for employees who won’t have to work on Thanksgiving day?

We are having a party and are putting square tables together in a long row for the party. We can put two chairs on each side of a table. The tables are all the same size. If we put together ten tables in a row, how many people can sit down?

In a group of 50 patrons 18 patrons like lattes 16 patrons like espressos and 8 patrons like both coffee drink how many patrons don’t like either of the coffee drinks

Mr Regpala needs the help of 6 students from the class to help him move some supplies. If the class has 31 students, in how many ways can the students be chosen to help?

A group has 9 teenagers and 10 adults. 6 of them 4 teenagers and 2 adults will ride in the shuttle together. How many ways are possible to shoose the 6 riders?