Math  /  Discrete

QuestionTen people are standing in line at a hamburger stand. In how many orders can the people stand?...

Studdy Solution

STEP 1

What is this asking? How many different ways can ten people line up? Watch out! Don't forget that the order matters here, so it's not just about picking people, it's about arranging them in a specific order.

STEP 2

1. Factorial Fun

STEP 3

We have **ten** spots in line.
The **first** person can be any of the ten people.
So we have 1010 choices for the first spot.

STEP 4

Now, for the **second** spot, we only have **nine** people left since one person is already in the first spot.
That gives us 99 choices for the second spot.

STEP 5

For the **third** spot, we have **eight** people left, giving us 88 choices.
We keep going like this until the very last spot.

STEP 6

For the **last** spot, there's only **one** person left, so we have 11 choice.

STEP 7

To get the **total number of ways** to arrange these ten people, we **multiply** the number of choices for each spot together.
This is because each choice for one spot can be combined with any choice for the other spots.
This gives us 1098765432110 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1.

STEP 8

This kind of multiplication is called a **factorial**, and it's written as 10!10!.
So, the number of ways ten people can stand in line is 10!10!.

STEP 9

**Calculate the factorial:** 10!=10987654321=3,628,80010! = 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 3,628,800

STEP 10

There are 3,628,8003,628,800 different ways for ten people to stand in line.
That's a lot of lines!

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord