Question

iv. what can i do with what i know?
tell whether each of the following is permutation or a combination. write each given on the
appropriate box. justify your answer by means of example.
determining the first, second, and third place in a contest
choosing friends to attend to a party
choosing household chores
assigning positions in a volleyball game
identifying telephone numbers of homes
arranging books on a shelf
forming triangle from 5 non - collinear points
selecting fruits to make a salad
forming two - digit number from 1, 2, 3, 6, and 7
forming subsets of a set

permutation\treason/example

combination\treason/example

v. what more do i need to know:

Answer:

To solve this, we recall: A permutation is an arrangement of objects where order matters, while a combination is a selection of objects where order does not matter.

Permutation (Order Matters)

1. Determining the first, second, and third place in a contest

• Reason: The order (1st, 2nd, 3rd) is important. E.g., if contestants are A, B, C, “A first, B second, C third” is different from “B first, A second, C third.”

1. Assigning positions in a volleyball game

• Reason: Positions (e.g., setter, spiker, libero) are distinct; order/role matters. E.g., assigning Player X to setter vs. spiker changes the arrangement.

1. Identifying telephone numbers of homes

• Reason: Telephone numbers are sequences where the order of digits matters (e.g., 1234567 vs. 7654321 are different numbers).

1. Arranging books on a shelf

• Reason: The order of books (e.g., Book A first, Book B second) matters. E.g., arranging “Harry Potter” then “Lord of the Rings” is different from the reverse.

1. Forming two - digit number from 1, 2, 3, 6, and 7

• Reason: The order of digits matters (e.g., 12 vs. 21 are different two - digit numbers).

Combination (Order Does Not Matter)

1. Choosing friends to attend a party

• Reason: The group of friends is what matters, not the order in which we choose them. E.g., choosing Alice and Bob is the same as choosing Bob and Alice.

1. Choosing household chores

• Reason: The set of chores is what matters, not the order of selection. E.g., choosing “wash dishes” and “do laundry” is the same as choosing “do laundry” and “wash dishes.”

1. Forming triangle from 5 non - collinear points

• Reason: A triangle is defined by a set of 3 points; the order of selecting the points does not change the triangle. E.g., choosing points A, B, C to form a triangle is the same as choosing B, A, C.

1. Selecting fruits to make a salad

• Reason: The combination of fruits is what matters, not the order of selection. E.g., selecting apple and banana is the same as selecting banana and apple.

1. Forming subsets of a set

• Reason: Subsets are defined by their elements, not the order in which elements are selected. E.g., the subset {1, 2} is the same as {2, 1}.

Filling the Table

Permutation Table

PERMUTATION	REASON/EXAMPLE
Assigning positions in a volleyball game	Positions (roles) are distinct; order of assignment matters (e.g., Player X as setter ≠ Player X as spiker)
Identifying telephone numbers of homes	Order of digits in the number matters (e.g., 1234567 ≠ 7654321)
Arranging books on a shelf	Order of books matters (e.g., Book A then Book B ≠ Book B then Book A)
Forming two - digit number from 1, 2, 3, 6, and 7	Order of digits matters (e.g., 12 ≠ 21)

Combination Table

COMBINATION	REASON/EXAMPLE
Choosing household chores	Set of chores matters, not order (e.g., wash dishes & do laundry = do laundry & wash dishes)
Forming triangle from 5 non - collinear points	Set of 3 points matters, not order of selection (e.g., Points A, B, C = Points B, A, C)
Selecting fruits to make a salad	Set of fruits matters, not order (e.g., apple & banana = banana & apple)
Forming subsets of a set	Set of elements matters, not order (e.g., {1, 2} = {2, 1})

If we were to present the answer in a more concise form for the table filling:

Permutation Entries (Row - by - Row)

• Row 1: Determining the first, second, and third place in a contest; Order of placement matters (e.g., A(1st), B(2nd) ≠ B(1st), A(2nd))
• Row 2: Assigning positions in a volleyball game; Order of positions (roles) matters (e.g., Player X as setter ≠ as spiker)
• Row 3: Identifying telephone numbers of homes; Order of digits in number matters (e.g., 1234567 ≠ 7654321)
• Row 4: Arranging books on a shelf; Order of books matters (e.g., Book A then Book B ≠ Book B then Book A)
• Row 5: Forming two - digit number from 1, 2, 3, 6, and 7; Order of digits matters (e.g., 12 ≠ 21)

Combination Entries (Row - by - Row)

• Row 1: Choosing friends to attend a party; Order of selection does not matter (e.g., Alice & Bob = Bob & Alice)
• Row 2: Choosing household chores; Order of selection does not matter (e.g., wash dishes & do laundry = do laundry & wash dishes)
• Row 3: Forming triangle from 5 non - collinear points; Order of point selection does not matter (e.g., Points A, B, C = Points B, A, C)
• Row 4: Selecting fruits to make a salad; Order of selection does not matter (e.g., apple & banana = banana & apple)
• Row 5: Forming subsets of a set; Order of element selection does not matter (e.g., {1, 2} = {2, 1})