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filaterals can you draw using the dots below as verti quadrilaterals possible in the previous problem are ns?

filaterals can you draw using the dots below as verti quadrilaterals possible in the previous problem are ns?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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4. How many triangles are there with vertices from the points shown below? Note, we are not allowing degenerate triangles - ones with all three vertices on the same line, but we do allow non-right triangles. Explain why your answer is correct. Hint 5. How many quadrilaterals can you draw using the dots below as vertices (corners)? Solution ... 6. How many of the quadrilaterals possible in the previous problem are: a. Squares? b. Rectangles? c. Parallelograms? d. Trapezoids? 2 e. Trapezoids that are not parallelograms?
Transcribed Image Text:4. How many triangles are there with vertices from the points shown below? Note, we are not allowing degenerate triangles - ones with all three vertices on the same line, but we do allow non-right triangles. Explain why your answer is correct. Hint 5. How many quadrilaterals can you draw using the dots below as vertices (corners)? Solution ... 6. How many of the quadrilaterals possible in the previous problem are: a. Squares? b. Rectangles? c. Parallelograms? d. Trapezoids? 2 e. Trapezoids that are not parallelograms?
Exercises 1. A pizza parlor offers 10 toppings. a. How many 3-topping pizzas could they put on their menu? Assume double toppings are not allowed. b. How many total pizzas are possible, with between zero and ten toppings (but not double toppings) allowed? c. The pizza parlor will list the 10 toppings in two equal-sized columns on their menu. How many ways can they arrange the toppings in the left column? Solution 2. A combination lock consists of a dial with 40 numbers on it. To open the lock, you turn the dial to the right until you reach a first number, then to the left until you get to second number, then to the right again to the third number. The numbers must be distinct. How many different combinations are possible? Solution 3. Using the digits 2 through 8, find the number of different 5-digit numbers such that: a. Digits can be used more than once. b. Digits cannot be repeated, but can come in any order. c. Digits cannot be repeated and must be written in increasing order. d. Which of the above counting questions is a combination and which is a permutation? Explain why this makes sense.
Transcribed Image Text:Exercises 1. A pizza parlor offers 10 toppings. a. How many 3-topping pizzas could they put on their menu? Assume double toppings are not allowed. b. How many total pizzas are possible, with between zero and ten toppings (but not double toppings) allowed? c. The pizza parlor will list the 10 toppings in two equal-sized columns on their menu. How many ways can they arrange the toppings in the left column? Solution 2. A combination lock consists of a dial with 40 numbers on it. To open the lock, you turn the dial to the right until you reach a first number, then to the left until you get to second number, then to the right again to the third number. The numbers must be distinct. How many different combinations are possible? Solution 3. Using the digits 2 through 8, find the number of different 5-digit numbers such that: a. Digits can be used more than once. b. Digits cannot be repeated, but can come in any order. c. Digits cannot be repeated and must be written in increasing order. d. Which of the above counting questions is a combination and which is a permutation? Explain why this makes sense.
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