Name ______Date ______

7.4ACC Practice HW-Counting Principle

1)Sofia has 4 shirts and 3 pairs of pants to choose from for her outfit. She can wear any shirt with any pair of pants. How many different outfits does Sofia have?
2)Astor went out to dinner with some friends. A full meal consists of an appetizer, a main course and a dessert. There were 2 choices of appetizers, 5 choices of main course and 3 choices for dessert. How many different meals can be made?
3)A bag contains the following digits: 2, 3, 5, 6, 8
You wish to create 2-digit ‘codes’ using these digits.
a)How many 2 digit codes can you create if you CAN use a digit more than once?
b)How many 2 digit codes can you create if you CANNOT use a digit more than once?
4)A bag contains the letters A, D, D, I, T, I, O, N
a)You create 2 letter codes by selecting a letter, writing it down, returning the letter to the bag, and then selecting another letter. How many possible 2-letter codes are there?
b)You create 3 letter codes by selecting a letter, writing it down. You do NOT return the letters to the bag as you go through the process of selecting. How many possible 3-letter codes are there?
5)Mary Ann is asked to create codes for an author who is writing a spy novel. She is told that the 3 character code must begin with a consonant and end with a vowel. The middle character must be a digit. There are 21 consonants and 5 vowels in our alphabet and 10 digits in our number system. How many different codes will Mary Ann be able to make?
6)You flip a coin and roll a (6 sided) die. How many possible combinations are there?
7)You wish to make ice cream sundaes for some friends. You buy 3 ice cream flavors: vanilla, chocolate, and strawberry. You also buy 2 types of sauces: fudge and raspberry. And finally, to top it all off, you buy whipped cream and sprinkles. If an ice cream sundae consists of ice cream, a sauce, and a topping, how many different sundaes are there?
8)You are given the following digits to create a 3-digit number:
2, 3, 6, 7, 8, 9.
a)How many 3-digit numbers can be created if a digit can be used more than 1 time?
b)How many 3-digit numbers can be created if you may NOT use a digit more than once?
c) How many 3 digit numbers can be created which are greater than 500?
9)Five students are playing musical chairs. Right now there are 4 chairs in a row. How many different ways could these 5 students be seated in these four chairs?