Finding Outcomes Answers

Three out of seven students in the cafeteria line are chosen to answer survey questions.How many different combinations of three students are possible?

How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen?

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?

Fiona chooses three towels from a group of five to pack in her beach bag for herself and her two brothers. Let the five towels be represented by A,B,C,D, and E.If Fiona chooses towel A for herself, which statements about the possible outcomes for her brothers’ towels are true? Select three options.There are 10 possible ways to choose the group of towels.The combination BC is not the same as CB.She has four choices for the first brother’s towel and three choices for the second brother’s towel.ABC, ABD, ABE, ACD, ACE, and ADE are the possible outcomes.If Fiona did not choose towel A for herself, there would be more outcomes.

A dance instructor chose four of his 10 students to be on stage for a performance.If order does not matter, in how many different ways can the instructor choose the four students?

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.Set X has 10 possible groupings.X YSet Y = {ABC, ABD, ABE, ACD, ACE, ADE}If person E must be in each group, then there can be only one group.There are three ways to form a group if persons A and C must be in it.

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?

Six teammates are competing for first, second, and third place in a race.How many possibilities are there for the top three positions?

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?

Evaluate the expression.4! • 3!

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?

Set V is all the unique three-digit numbers using the digits 1, 2, 3, 4, and 5.Which set would be considered a subset of set V?