SCAVONE 7. Suppose we have 11 total books to put on a shelf. 6 of the books are

Question

SCAVONE 7. Suppose we have 11 total books to put on a shelf. 6 of the books are red, 3 of the books are blue, and 2 of the books are yellow. Determine the following. Show your work! a. In how many ways can the books be ordered on the shelf with no restrictions? Answer In how many distinguishable ways can the books be ordered on the shelf if books of the same color are identical? b. Answer 8. First indicate if each of the following is a permutation or a combination (CIRCLE ONE). Then calculate the number. (You may use the calculator function to calculate.) How many possible committees of 5 people can be selected from a club of 18? a. PERMUTATION COMBINATION Number b. Mrs. Nelson needs 3 students to help clean her classroom: student 1 to sweep the floors, student 2 to clean off the desks, and student 3 to wash the chalkboards. In how many different ways can she select 3 students to help from her class of 24? PERMUTATION COMBINATION Number In how many different ways can the gold, silver, and bronze medals be awarded among 7 competitors in a sporting event (assuming there are no ties)? c. PERMUTATION COMBINATION Number Terry has 14 lottery tickets and you paid for 4 of them. How many possible groups of 4 tickets can you choose from Terry's 14? d. PERMUTATION COMBINATION Number c. A softball team has 13 players. How many 9-player batting orders are possible? PERMUTATION COMBINATION Number

Explanation / Answer

7)A) Number of ways to arrange 11 books =11! =39916800

b) ways to arrange so that all of same color are identical =11!/(6!*3!*2!) =4620

8a)

combination:

number =18C5 =8568

b)

permutation:

number =24P3 =12144

c)

permutation:

number =7P3 =210

d)

combination:

number =14C4 =1001

e)

permutation:

number =13P9 =259459200

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