Question

in a collection of 10 voters, how many different coalitions are possible?

Answer 1

@ikileyxx Are you familiar with the counting principle of multiplication?

Answer 2

Yes @Hero

Answer 3

Okay, so how do you think it would pply it in this case?

Answer 4

I know you would multiply, I just don't know by what. @Hero

Answer 5

In this case, if you are trying to find the number of possible arrangements of \(n\) objects, then the total number of possible arrangements is \(n!\) or \(n\) factorial.

Answer 6

So would it be 10 factorial? Or is that completely wrong? lol

Answer 7

Yes, 10 factorial is correct. Do you know how to write 10! in expanded form?

Answer 8

3628800

Answer 9

That's the calculated form. I suppose you don't know how to write 10! in expanded form.

Answer 10

I do not.

Answer 11

10! = (10)(9)(8)(7)(6)(5)(4)(3)(2)(1)

Answer 12

Ah, that's what I thought but I assumed it wasn't right.

Answer 13

Yeah, there has to be a way to calculate 10! by hand. One day you might wake up in a world where calculators and computers no longer function or exist. If that happens, you'll still know how to calculate 10 factorial without them.

Answer 14

Hahaha, great point. So for this question would the answer just be the calculated form?

Answer 15

Well, the usual way to show your work is to write a complete solution which would show how you reasoned your way to the answer. It would include things such as the related concept (n factorial), your calculations by hand (expanded form of n factorial), the calculated form and then what the calculated result means in a sentence.

Answer 16

Great! Thanks so much, very appreciated.

Answer 17

yw