Finding Outcomes Answers

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.

Evaluate the expression.4! • 3!

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?

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

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

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?

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?

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?

Holly chooses seven out of nine plants for the front of her house with the remaining plants to be used on the side of the house.If order does not matter, in how many ways can she choose the plants for the front of the house?