For this problem, assume that you are to pick 4 cars from the motor pool, which contains 7 subcompact cars, 4 compact cars, and 6 midsize cars. How many ways can you pick the cars so not all are the same size?

The president of the college asked a fraternity to submit a list of 7 students to serve as guides at a school function. They have 19 students who are Available to help. In how many ways can the students be chosen?

Your sister is shopping at an exclusive Rodeo Drive clothing store and examines 4 distinct blouses, 5 distinct dresses, and 2 distinct handbags. How many different combinations of items can she purchase if she buys exactly 2 blouses, 3 dresses and 1 handbag?

A landscaper has 8 different flowering plants. She needs to plant 4 of them in a row in agarden. How many different ways can 4 of the 8 plants be arranged in a row?

There is a town party in Pleasantville where 6 families of 3 people each get together. If one representative from each family gives a gift to everyone at the party except people from their own family, how many gifts in total are given?

Three hungry pirates, Ahab, Bluebeard, and Hook, were stranded on a desert island. They came upon a treasure chest, which they immediately opened. To their joy, they found it to be full of pretzels! Immediately they each ate 10, then they decided they should save the rest for later. That night, after the others had fallen asleep, Ahab crept to the treasure chest and opened it. He separated the pretzels into 3 equal piles. There was 1 extra pretzel, which he gave to a passing monkey. Then he stole one of the 3 equal piles of pretzels, put the rest back into the chest, and went back to camp. A short time later Bluebeard sneaked over to the chest. He separated the pretzels into four equal piles (he wasn’t quite as greedy as Ahab). There were 2 extra pretzels, which he gave to a passing monkey. He then stole one of the four piles and put the rest back into the chest. Still later Hook went to the chest and separated the pretzels into five equal piles. There were 3 left over, which he gave…

How many committees can be formed from 12 men and 12 women if the committee must consist of 3 men and 4 women?

From a league of 25 players, we want to choose 11 players for a football match. A goalkeeper, a captain and 9 players. In how many ways we can arrange the team?

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?

Of the first 5 vehicles in the teacher’s parking lot last Tuesday, 2 of them were minivans. Based on this information, if there are 120 vehicles in the parking lot, how many would you expect to be minivans?