Finding Outcomes
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
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?
a- 252 b- 126
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?
a- 6,840 b- 342 c- 18
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 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 represents the number of ways the group can be chosen. In how many ways can the group be chosen?
a- 720 b- 30 c- 20
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. a- The combination of AB and BA are the same. b- Each shirt can be paired with any one of other the remaining shirts. c- There are twenty possible ways to choose the group of shirts. d- He has five choices for the first shirt and five choices for the second shirt. e- If he chooses shirt B, there are four possible outcomes for choosing the second shirt.
a- The combination of AB and BA are the same. b- Each shirt can be paired with any one of other the remaining shirts. e- If he chooses shirt B, there are four possible outcomes for choosing the second shirt.
In how many ways can the letters in the word balloon be arranged? a- 210 b- 1,260 c- 2,520 d- 5,040
b- 1,260
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? a- 21 b- 35 c- 56 d- 70
b- 35
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? a- ABC b- ABC, BAC, CBA c- AAA, BBB, CCC d- ABC, ACB, BCA, BAC, CAB, CBA
d- ABC, ACB, BCA, BAC, CAB, CBA
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 a- Her work is correct. b- Her answer is correct. c- In step 1, the subtraction cannot be completed before the factorial of each number is calculated. d- In step 1, 12! divided by 10! is not equivalent to 6! divided by 5!. e- In step 3, the dividing out of common factors was performed incorrectly. f- There are sixty-six ways to choose ten items from twelve.
d- In step 1, 12! divided by 10! is not equivalent to 6! divided by 5!. f- There are sixty-six ways to choose ten items from twelve.
