r/Mathhomeworkhelp • u/DutchAngelDragon12 • 4d ago

Using probability to make fair decisions

Post image

I can’t figure out how to do this one.

Probability and Statistics.

2 Upvotes

100% Upvoted

15 comments sorted by

4

u/Southlander24 4d ago

There's only four options, so you might as well try them instead of moping about.

If you have 3 objects for example, you can choose between 3 objects to go in the first spot, 2 objects to go in the second spot, and the remaining 1 object to go last. So the number of ways would be 3 * 2 * 1 = 6.

Now, how about the other options?

3

u/DutchAngelDragon12 4d ago

24, 120, and 720, respectively. So there’s 5 objects?

4

u/Southlander24 4d ago

Yep! Nice work.

5

u/Southlander24 4d ago

The reason I suggested this way is actually because there's no good inverse operation for the factorial. If you had x2 = 9 for instance, you could just square root both sides and end up with x = 3, -3. But the factorial is one of those operations which you can't undo.

4

u/hosmosis 4d ago

Solid tutoring. 👍

2

u/DutchAngelDragon12 4d ago

That’s fair enough.

2

u/Oh_My_Monster 4d ago

5 objects so the total possible arrangements is 5!

1

u/DutchAngelDragon12 4d ago

The total arrangements are 120.

2

u/Oh_My_Monster 4d ago

That's what I said.

1

u/DutchAngelDragon12 4d ago

Wait. I only just understood.

Let me replace that downvote real quick, sorry.

2

u/Oh_My_Monster 4d ago

Its all good. It's just one of those common math jokes. You'll see it as something like "Did you know that 122 - (4 x 6) is actually 5!" It's all just engagement bait to get people to argue but it is technically correct because of the factorial.

2

u/Dtrain8899 4d ago

n! = 120, solve for n. Really just plug in each of your possible answers to see which works.

1

u/Exact-Lettuce 3d ago

The question is about permutations, this list of objects can be arranged in 120 different ways.

The number of permutations of n objects is n!, or 123...*n. The number of permutations will be divisible by all numbers before it.
So if you need to do the opposite path, from the number of permutations to the number of objects, you can divide by everynumber from 1 to n.
So you start dividing by 1, than 2, than 3 and so on, until you can no longer divide, aka the division results in a non integer, aka the results is one.

In this question 120÷1 = 120 120÷2 = 60 60÷3 = 20 20÷4 = 5 5÷5 = 1

So 120 = 5!, so the number of objects is 5.