Question

A display case has room for 10 statues. Find the number of ways you can line up the statues if you have 5 statues

Answer 1

(Just and Example so it'll kinda explain it.)

Example A

How many ways can 5 students sit in a row?

Solution: If we consider the students sitting in one of five seats, then we have 5 students to choose from for the first seat, four remaining to choose from for the second seat and so on until all the seats are filled.

5–×4–×3–×2–×1–=120 So there are 120 ways to seat the students.

More Guidance

The way we just wrote out 5–×4–×3–×2–×1– can also be expressed as a factorial. A factorial is the product of a number with each number less than itself. We use the notation, 5!, which is read as “five factorial” to represent the expression 5–×4–×3–×2–×1–. It is important to note that 0!=1!=1. Students are often perplexed that both zero and one factorial are equal to one but think back to the context for illustration. If you want to arrange zero items, how many ways can you do it? If you want to arrange one item, how many ways can you do it? There is only one way to “arrange” zero or one item.

To evaluate a factorial on the TI-83 or 84 graphing calculator, type in the number, then press MATH→NUM, 4!. Press ENTER to evaluate.