Chapter3 Exercises Ca NTING Problems 11 through 15 offer practice wih the combin
ID: 3277925 • Letter: C
Question
Chapter3 Exercises Ca NTING Problems 11 through 15 offer practice wih the combinations rule. 11. How many ways can two people be chosen from a group of 10 people? 12. How many ways can three pizza toppings be selected from a choice of 8 pizza toppings? 13. How many ways can five eggs be selected from a basket of 12 distinct Easter eggs? 14. How many ways can a 9-person baseball team be chosen from among a roster of 15 people? How many ways can 12 books be selected from a shelf of 20 books? A string of 7 characters is formed by ordering the letters ABCDEFG. b. How many strings begin and end with a vowel? 15 16. How many strings are possible? a. How many strings contain the substring ACE? How many strings contain both substrings AB and FG? C. d. 17.A Halloween bag contains 10 Snickers bars, 6 Mars bars, and 5 Crunch bars. a.How many ways can a child select three bars from the bag? b. How many ways can a child select one of each type of bar? c.How many ways can a child select two of each type of bar? Consider an 8-bit string consisting of 0's and 1's. a. b. 18. How many possible strings are there? How many strings contain exactly three 1s? c. How many strings begin and end with a 1? d.How many strings contain at least one 1?Explanation / Answer
11. Number of ways in which 2 people can be chosen from 10 = 10C2
= 10! / (8! X 2!)
= 10x9/2
= 45 ways
12. Number of ways of chosing pizza toppings = 8C3
= 8! / (5! X 3!)
= 8x7x6/3x2
= 56 ways
13. Number of ways in which 5 eggs can be selected from 12
= 12C5
= 12! / (7! X 5!)
= 792
14. Number of ways of selecting basketball team = 15C9 = 5005
15. Number of ways of selecting books = 20C12 = 125970
P.S - 5 questions are answered here. Please post the remaining ones separately