SUMMATIVE TEST 3 Q3

A school principal is arranging 6 different awards on a display shelf where the order in which they are placed matters. What mathematical concept is used to determine the number of possible arrangements?

• Combination

• Permutation

• Probability

• Factorization

A school is assigning seats to students for an examination, where each seat has a specific number. Which of the following best illustrates this situation?

• Selecting 5 students to join a competition

• Choosing 3 books from a library to read

• Assigning numbered seats to students for an exam

• Forming a study group with 4 members

A librarian is organizing 7 different books on a shelf and calculates the total number of ways to arrange them by multiplying all positive integers up to 7. What is this product called?

• Powers of 7

• Multiples of 7

• 7-factorial

• 7-factors

A teacher explains that P(n,r) represents the number of ways to arrange r objects chosen from n distinct objects when order matters. Why is P(n,r) equal to n!(n−r)! ?

• Because order does not affect the arrangement.

• Because P(n,r) is derived from n! divided by the ways to arrange the unchosen objects, which is (n−r)!.

• Because permutations are always equal to factorial values.

• Because P(n,r) is undefined when r=0

A student is asked to calculate P(5,5), which represents the number of ways to arrange 5 objects in a specific order. What is the result of P(5,5)?

• 10

• 60

• 120

• 240

A concert hall has 10 available seats in the front row, and 6 musicians are to be arranged in those seats for a performance. How many different ways can the 6 musicians be arranged in the 10 seats?

• 2520, because only 6 seats are available for selection

• 5040, because 10 musicians are being arranged in 6 positions

• 30240, because the number of arrangements is calculated as P(10,6)=10×9×8×7×6×5

• 3628800, because the total number of arrangements is found by multiplying 10!

In a contest, the number of ways to arrange r students out of 8 is given by P( 8, r). The teacher wants you to determine the value of r based on this information. What is the value of r?

• 3, because P(8,3)=336

• 4, because P(8,4)=1680

• 5, because P(8,5)=6720

• 6, because P(8,6)=20160

Which of the following is an example of a situation where the order of selection does not matter?

• Assigning seats to students in a row

• Selecting 3 committee members from a group of 10

• Arranging trophies on a display shelf

• Creating a password using four different digits

You are given several different tasks to complete. Some tasks require a specific order, while others do not. Which of the following scenarios does not illustrate a combination, where the order does not matter?

• Choosing three subjects to study for an exam

• Selecting toppings for a pizza

• Arranging books in a specific order on a bookshelf

• Picking flowers for a bouquet

A school is selecting a president, vice president, and secretary from a group of students. Which of the following statements correctly describes a characteristic of this selection process?

• The order matters when assigning roles.

• The order does not matter when assigning roles.

• The students can switch roles without changing the outcome.

• The selection process is based only on the number of students chosen, not their positions.