Finding Outcomes

In how many ways can the letters in the word balloon be arranged?

1,260

A physical education class has 16 students. How many ways are there to create a four-person team for a game? One person leaves the class and the teacher must decide between creating teams of three or teams of five. Which phrase completes the statement? The number of possible teams of three is the number of possible teams of five.

1,820 less than

A librarian chooses seven holiday books from a selection of ten to be displayed in the window of the library. In how many different ways can she choose the group of seven books?

120

There are eleven people on a softball team and nine different positions. Work through the questions to determine how many ways a coach can choose the players for the positions if Amy does not want to pitch. If there are eleven people on the team and nine positions, how many total arrangements of the players can be made?____ If Amy does not want to play pitcher, then there are now _____ people available to pitch. Assuming the pitcher has already been chosen, there are ten remaining players and ______ remaining positions. How many ways are there to arrange the remaining players and positions?

19,958,400 10 8 1,814,400

Ten students need to present their reports. Five can present each day. How many ways can the teacher choose a group of five students to present their reports on the first day? How many ways can the teacher choose a group of 5 students to present on the first day if Marjorie must present on the first day?

252 126

Juan is making a fruit salad. He has grapes, watermelon, apples, pineapple, bananas, mangoes, honeydew, and cantaloupe. He wants his fruit salad to contain five different fruits. How many ways can he make the fruit salad if it must contain watermelon?

35

At a gymnastics meet, twenty gymnasts compete for first, second, and third place. How many ways can first, second, and third place be assigned? Third place has been announced. In how many ways can the remaining two places be assigned? Third and second places have been announced. In how many ways can first place be assigned?

6,840 342 18

Evaluate each expression 6!= 3! • 2! = 6!/3!=

720 12 120

The number of ways six people can be placed in a line for a photo can be determined using the expression 6!. What is the value of 6!? Two of the six people are given responsibilities during the photo shoot. One person holds a sign and the other person points to the sign. The expression 6!/(6-2)! represents the number of ways the two people can be chosen from the group of six. In how many ways can this happen? In the next photo, three of the people are asked to sit in front of the other people. The expression 6!/(6-3)!3! represents the number of ways the group can be chosen. In how many ways can the group be chosen?

720 30 20

At the airport, ten people are waiting on standby. Two seats become available, one first class and one coach. How many ways are there to fill the two seats?

90

Three students, Angie, Bradley, and Carnell, are being selected for three student council offices: president, vice president, and treasurer. In each arrangement below, the first initial of each person's name represents that person's position, with president listed first, vice president second, and treasurer third. Which shows the possible outcomes for the event?

ABC, ACB, BCA, BAC, CAB, CBA

A committee of four is formed from five eligible members. Let the eligible members be represented with A, B, C, D, and E. The possible outcomes include S = {ABCD, BCDE, ACDE, ABCE, ABDE}. Which statements about the situation are true? Check all that apply.

If persons A and C must be on the committee, there are three ways to form the committee. If the number of eligible members increases, the number of outcomes increases.

Lorelei evaluates the expression to determine how many different groups of ten she can make out of twelve items. Her solution: 1). Subtract within parentheses and simplify: 6!/(2)!5! 2). Expand: 6∙5∙4∙3∙2∙1/2∙1∙5∙4∙3∙2∙1 3). Divide out common factors: 6/2∙1 4). Because 6 divided by 2∙1 is 3, there are 3 ways to choose the groups. Which statements describe Lorelei's solution? Check all that apply

In step 1, 12! divided by 10! is not equivalent to 6! divided by 5!. There are sixty-six ways to choose ten items from twelve.

Eli chooses two shirts from a group of five to pack for a weekend trip. Let each shirt be represented by A, B, C, D, and E. Which statements about the situation are true? Check all that apply.

The combination of AB and BA are the same. Each shirt can be paired with any one of other the remaining shirts. If he chooses shirt B, there are four possible outcomes for choosing the second shirt.

A teacher has four books—A, B, C, and D—to assign to four students in any order he prefers. Set S includes all possible arrangements of the four books. Set X includes all possible arrangements when book C is chosen first and D is chosen second. Which notation is correct? ______ c ______ If book C is chosen first and D is chosen second, in how many ways can the teacher assign the books? _______

X S 2