Can someone please help? I'll give you a medal if you can explain some about this for me!
A college student purchased 10 posters for her dorm room, but she only has space to hang six of them. How many specific ways can she arrange and hang these six posters on her wall?
60
8
151,200
210

Question

amistre64 · Answer

how many choices are there for the first poster?

anonymous · Answer

Six? Sorry, I have no idea how to do this.

amistre64 · Answer

if you have 10 posters to choose from,  then you have 10 choices for the first poster ..... agreed?

anonymous · Answer

Yes.

amistre64 · Answer

so, after you make your first choice, how many choices do we have remaining for the 2nd poster?

anonymous · Answer

Nine

amistre64 · Answer

good, if we count this ... we have 10 ways to make 9 choices.  10*9

now,  after we make the first 2 choices, how many choices are left for the 3rd poster?

anonymous · Answer

Eight, and then seven, et cetera.

amistre64 · Answer

lol, good youre catching on.

we have 10 ways to have 9 ways to have 8 ways to have 7 ways to have 6 ways have 5 ways to pick the posters ..... 

we have 10*9*8*7*6*5 ways to pick an arrangement of 6 posters from 10

anonymous · Answer

Oh, that makes sense.  The first thing I tried was 10! and that didn't sound right.

amistre64 · Answer

yeah, 10! is to big.  10! is the number of ways to hang 10 posters in 10 different ways :)

amistre64 · Answer

10P6  is what we want fer sure

anonymous · Answer

So the answer is 151,200?

anonymous · Answer

Thank you so much!

amistre64 · Answer

yes, and youre welcome

anonymous · Answer

How does one give a medal, anyway?

anonymous · Answer

Ah, I got it.