Question

in the scenarios below, select all scenarios where order matters:
□ selecting 11 people to serve on a jury when the pool of jurors contains 200 people.
□ select 5 books to assign as readings for the year out of a list of 100 books.
□ creating a 4-digit pin for your debit card.
□ selecting a 6-digit lock combination where the digit \0\ cannot be used.
□ choosing four people out of ten to serve on a committee.
□ choosing 5 students to represent the school at a district function.

question 2 (1 point)
as part of a marketing campaign for a small restaurant they want to show off the number of different meals a person can have if they order an appetizer, salad or soup, an entree, and a dessert. on the menu they have 4 appetizers you can order, 3 salads, 4 soups, 12 entrees, and 3 desserts.

how many different total meal combinations can be made?

your answer:

answer

question 3 (1 point)
there are 6 true-or-false questions on an exam. in how many ways can a student answer those questions if each must have an answer?

your answer:

Explanation:

Question 1

Order matters when the sequence/arrangement of items changes the outcome. For jury, book selections, committee, and student representatives, the group composition is what matters, not the order of selection. For PINs and lock combinations, different digit sequences create distinct codes, so order matters.

Step1: Calculate salad/soup options

Add salad and soup counts: $3 + 4 = 7$

Step2: Multiply all meal components

Multiply appetizers, salad/soup, entrees, desserts: $4 \times 7 \times 12 \times 3$

Step3: Compute final total

Calculate the product: $4 \times 7 = 28$; $28 \times 12 = 336$; $336 \times 3 = 1008$

Step1: Identify per-question options

Each question has 2 choices: $2$

Step2: Calculate total combinations

Raise options to number of questions: $2^6$

Step3: Compute final value

Calculate the power: $2^6 = 64$

Answer:

• Creating a 4-digit PIN for your debit card.
• Selecting a 6-digit lock combination where the digit "0" cannot be used.

---

Question 2