Homework Problems for Counting

1.    A ski store has 20 different boots available, 50 different pairs of skis, and 9 different hats.   In how many different ways can a customer purchase an item from the store?


2.    A ski store has 20 different boots available, 50 different pairs of skis, and 9 different hats.   In how many different ways can a customer purchase a set of skis, boots and a hat from the store?


3.    A tennis shoe company makes 4 different pairs of running , 5 different pairs of walking and 3 different pairs of court shoes.   If a pair of shoes consists of a running, walking and court shoe, how many different ways can a pair of shoes be bought?


4.    A tennis shoe company makes 4 different pairs of running , 5 different pairs of walking and 3 different pairs of court shoes.   In how many different ways can a pair of shoes be bought?


5.    A high school student has been offered a summer job at 5 grocery stores, 4 gas stations, 7 fast food chains, and 3 dry cleaners.   How many choices of jobs are possible?


6.    A high school student has been offered a summer job at 5 grocery stores, 4 gas stations, 7 fast food chains, and 3 dry cleaners.   How many different ways are there for the student to accept a job at a grocery store, a gas station, a fast food chain and a dry cleaners?


7.    At Ron's cafe, lunch consists of a choice of:   burrito, sandwich, soup or hamburger.   A choice of french fries or coleslaw, and a choice of coke or juice.   In how many different ways can lunch be ordered?


8.    A student must take a History, Math and English class.   There are 8 different History classes to choose from, 5 different Math classes, and 2 English classes.   In how many ways can this be accomplished?


9.    A local union is to elect a president, secretary and treasure.   No member can win more than one seat.   If there are 75 union members, how many outcomes can the election have?


10.    A local union is to elect a president.   If there are 75 union members, how many outcomes can the election have?


11.    If there are seven questions on a true false exam, how many different outcomes for the test can occur?


12.    If there are seven questions on a multiple choice exam, and there are four choices for each question, how many different outcomes for the test can occur?


13.    In a certain country, television stations names contain either three or four letters and must start with either the letters R or Y.   How many station names are available with this criteria?


14.    In a certain country, television stations names contain either three or four letters and must start with either the letters R or Y.   How many station names are available if the names end with B?


15.    In a certain country, television stations names contain either three or four letters and must start with either the letters R or Y.   How many station names are available if the names end with B or N?


16.    In a certain country, television stations names contain either three or four letters and must start with either the letters R or Y.   How many station names are available if the names do not contain any repeated letters?


17.    In a certain country, television stations names contain either three or four letters and must start with either the letters R or Y.   How many station names are available if the names end with B or N and do not contain any repeated letters?


18.    There are 4 dogs and 4 cats.   In how many different orders can these animals be placed in line under the following conditions?
A)   Any animal can be next to any other animal.
B)   The dogs and cats are lined up alternately.
C)   The first and last animal in line must be a cat.
D)   All the dogs are together, and all the cats are together.
E)   The two positions in the middle of the line must be filled by dogs.

19.    Two scholarships are to be awarded to students in the science department.   There were 4 chemistry majors, 2 math majors, and 5 physics majors who applied for the scholarships.   If the scholarships are the same, how many different ways can the scholarships be given to any student?


20.    Two scholarships are to be awarded to students in the science department.   There were 4 chemistry majors, 2 math majors, and 5 physics majors who applied for the scholarships.   If the scholarships are different, how many different ways can the scholarships be given to two different students?


21.    Two scholarships are to be awarded to students in the science department.   There were 4 chemistry majors, 2 math majors, and 5 physics majors who applied for the scholarships.   If the scholarships are different, how many different ways can the scholarships be given to students with different majors?


22.    Two scholarships are to be awarded to students in the science department.   There were 4 chemistry majors, 2 math majors, and 5 physics majors who applied for the scholarships.   If the scholarships are the same, how many different ways can the scholarships be given to students with different majors?


23.    A group of 4 doctors, 8 teachers, and 6 business leaders are going to form a committee of two.   How many different ways can the committee be formed with people from different professions?