Mr. Watts’s MTH 110 class organizes a club devoted to making…

Mr. Watts’s MTH 110 class organizes a club devoted to making tests like this one less silly. There are 13 people in the class. Suppose the club decides to elect two officers (president, vice president) and form two executive committees—a 3-person planning committee and a 4-person silliness reduction committee. How many ways can they do this?

Pinky Burwinkle’s is making good progress in its quest to he…

Pinky Burwinkle’s is making good progress in its quest to help reduce the environmental damage caused by evil packs of rogue kittens. Once in the forest, she hands out hatchets to help students clear the underbrush so that they can address the massive ecological damage caused by rogue bands of evil kittens. From the 10 students she trusts, she chooses five to give hatchets to. However, the tools are in five different sizes (child size, small, medium, extra-medium, and large) so it matters who gets which hatchet. (NOTE: DO NOT GIVE HATCHETS TO SMALL CHILDREN) In how many ways can she hand out the tools?

Pinky Burwinkle’s second grade class is going on a field tri…

Pinky Burwinkle’s second grade class is going on a field trip to the national forest help reduce the environmental damage caused by evil packs of rogue kittens. Most of them (the students, not the kittens are in detention, so only 11 of them got to go on the trip. Miss Burwinkle decides to line them up and march them all to the bus. In how many different orders can she line up the students?