Math II - Finding Outcomes Quiz 100% CORRECT

Set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three. Set Y is made up of the possible ways five students can be formed into groups of three if student A must be in all possible groups. Which statements about the situation are true? Select three options. A) Set X has 10 possible groupings. B) X Y C) Set Y = {ABC, ABD, ABE, ACD, ACE, ADE} D) If person E must be in each group, then there can be only one group. E) There are three ways to form a group if persons A and C must be in it.

A) Set X has 10 possible groupings. C) Set Y = {ABC, ABD, ABE, ACD, ACE, ADE} E) There are three ways to form a group if persons A and C must be in it.

A membership committee of three is formed from four eligible members. Let the eligible members be represented by A, B, C, and D. The possible outcomes include S = {ABC, ABD, ACD, BCD}. Which statements about the situation are true? Select three options. A) There are four ways to choose the committee. B) There are three ways to form the committee if person D must be on it. C) If seven members are eligible next year, then there will be fewer combinations. D) If persons B and C must be on the committee, there are two ways to form the committee. E) If persons A and C must be on the committee, then there is only one way to form the committee.

A) There are four ways to choose the committee. B) There are three ways to form the committee if person D must be on it. D) If persons B and C must be on the committee, there are two ways to form the committee.

How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen? A) 100 B) 120 C) 240 D) 720

B) 120

Fiona needs to choose a five-character password with a combination of three letters and the even numbers 0, 2, 4, 6, or 8. If she uses her initials, F, J, and S in order as the first three characters, and she does not use the same digit more than once in her password, how many different possible passwords are there? A) 10 B) 20 C) 24 D) 40

B) 20

Eight students are competing for a blue, red, and yellow ribbon for their agriculture project. How many different ways are there to present those ribbons if the order matters? A) 56 B) 336 C) 6,720 D) 8,064

B) 336

Three out of seven students in the cafeteria line are chosen to answer survey questions. How many different combinations of three students are possible? A) 7 B) 35 C) 70 D) 210

B) 35

Evaluate the expression. 4! • 3! A) 12 B) 30 C) 144 D) 5,040

C) 144

Three out of nine students in the computer club are getting prizes for first, second, and third place in a competition. How many ways can first, second, and third place be assigned? A) 3 B) 84 C) 504 D) 2048

C) 504

Helena has five different flowers. She plans to give one flower to each of her five teachers in any order. She gives the first flower to one of her teachers in the morning. In how many different ways can she give the four remaining flowers to the rest of the teachers in the afternoon? A) 1 combination B) 4 combinations C) 21 combinations D) 24 combinations

D) 24 combinations

Four band members, Harry, Isabel, Jose, and Karen, are all boarding a bus to attend a concert. In each arrangement below, the first initial of each person's name represents that person's position as he or she boards the bus: first, second, third, and fourth. If we know that Karen boards the bus first, which shows the possible outcomes for this event? A) KHIJ B) KHIJ, KHJI C) KHIJ, KHJI, KJHI, KJIH D) KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH

D) KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH