Alfred is opening a new office and needs to decorate and furnish it. He has 3 sources for wallpaper, 2 sources for carpet, 6 sources for drapes, 5 sources of furniture, and 8 sources for pictures. How many ways can he select one of each

Mike wants to know how many different outfits he can make out of his business wardrobe. He has 7 pairs of trousers, 16 shirts, 4 jackets, 18 ties, and 5 pairs of shoes. How many different outfits does he have if he always wears trousers with a shirt, a jacket, a tie, and a pair of shoes?

A bag of lollipops is shared among a group of children, where each child receives 10 lollipops. 6 more children join the group and the teacher bought 20 more lollipops to share with all the children. In the end, each child receives 8 lollipops. How many children are there now?

John has 9 boxes of apples. Each box holds 12 apples. If 6 of the boxes are full, and 3 of the boxes are half full, how many apples does John have?

The number of ways 3 nurses and 4 engineers can be seated on a bench with the nurses seated together is

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 medical salesperson is to visit the various members of the staff at a clinic. He must see 8 doctors, 6 physicians assistants, 12 nurses, 3 medical technologists, and 3 receptionists. How many different ways can these people be visited by the salesperson if the order is not important?

Twenty children are to be divided into an X team and a Y team of 10 each. The X team will play in one league and the Y team in another. How many different divisions are possible?

Albright, Becker, Chalmers, Dawkins, and Earl all entered the primary to seek election to the city council. Albright received 2000 more votes that Becker and 4000 fewer than Chalmers. Earl received 2000 votes fewer than Dawkins and 5000 votes more than Becker did. In what order did each person finish in the balloting?

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?