match each with correct solution: (1) Video store has 8 new releases this week.
ID: 3105468 • Letter: M
Question
match each with correct solution:(1) Video store has 8 new releases this week. Each is available on videotape and DVD. How many ways can a customer choose a new release and a format to rent?
(2) 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?
(3) 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 two essays?
(4) An ice cream shop offers a choice of two types of cones and 15 flavors of ice cream. How many different one scoop ice cream cones can a customer order?
(a) 940 (b) 30 (c) 240 (d) 20 (e) 16
Explanation / Answer
1. 8 movies times 2 formats for each movie = 16 ways the customer can choose 2. The dictionary is d and the other books are x. Then the bookshelf can either be: dxxxxx or xxxxxd. The dictionary can only be in two places. The other five books must be placed in one of the five spots. For the first spot, we have five choices. For the second, we have four choices, and so on. This leads to a total of 5!, or 5*4*3*2*1 = 120. 120 * 2 (for the dictionary placement) is 240 different ways to arrange the books. 3. Since the essays are different, order matters. Therefore, we have 5 choices for the short essay and 4 choices for the long essay. 5*4 = 20 ways she can choose the topics. 4. There are 15 flavors to choose from, and 2 cones to choose from. 15 * 2 = 30 different one-scoop cones a customer can order.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.