Algebra 2 CP Help!! Answer ASAP

1. For a college application, Macawi must select one of five topics on which to write a short essay. She must also select a different topic from the list for a longer essay. How many ways can she choose the topics for the two essays?

2. An ice cream shop offers a choice of two types of cones and 15 flavors of ice cream. How many different 1-scoop ice cream cones can a customer order?

3. A video store has 8 new releases this week. Each is available on videotape and on DVD. How many ways can a customer choose a new release and a format to rent?

4. How many ways can six different books be arranged on a shelf if one of the books is a dictionary and it must be on an end?

Answers to Choose From:
20
940
30
240
16

1. For the first essay, she has 5 choices. For the second essay, she has four (because one is gone from the first selection). Thus, there are 5 * 4 = 20 ways to choose.

2. There are 15 choices of flavor, and 2 choices of cones. Thus, there are 15 * 2 = 30 choices overall.

3. There are 8 releases and 2 ways to purchase each release. Thus, there are 8 * 2 = 16 choices.

4. There are six books, and you know the dictionary must be on an end. First consider the case where the dictionary is first. There is only one book for the first space, the dictionary. There are 5 choices for the second space, 4 choices for the third space, 3 choices for the fourth space, 2 choices for the fifth space, and 1 choice for the last space. Multiply these to get 1 * 5 * 4 * 3 * 2 * 1 = 120 choices. Now, we consider the case where the dictionary is last. This would produce the same amount of choices, 120. Add these two numbers to get 120 + 120 = 240 choices overall.

Answers:
1. 20
2. 30
3. 16
4. 240

1. 5 P 2. As she choose two essays where choosing essay1 to be long and choosing essay2 to be short is NOT the same as choosing essay 1 to be short and choosing essay2 to be short. There are 5*4 = 20 ways of choosing two essays