You have a bucket that has 8 balls in it, numbered from 1 through 8. Show that the number of ways you can draw out the 8 is 40,320. (Remember - how many ways can you draw the first number? THEN, how many ways can you draw the second number? And so on...)

Question

majikdusty · Answer

Are you familiar with the symbol ! in mathematics? This is called a factorial. It's used liked this. 8! = 8*7*6*5*4*3*2*1 which is indeed equal to 40,320

majikdusty · Answer

When you have a scenario where the things being drawn can only be drawn once (ball 1 can't be drawn two times) then you use factorial.

anonymous · Answer

Yes, but my teacher wants us to write it out the long way

anonymous · Answer

Which I do not know how to

majikdusty · Answer

hmm that is more tricky, but this is how i think about it. 

you can draw either 1-8 for the first number correct?
When you go to draw the second ball, there are only 7 choices left
Then the next time you draw there are only 6 possible balls left (because two are drawn)
this pattern continues. 
then you get the 8*7*6... ect

Is this thought process more or less what your teacher is looking for?

anonymous · Answer

Thank you, I think that  is what she is looking for. Is that 'the box method'

majikdusty · Answer

Honestly I'm not exactly sure if that is 'the box method', but to me it is the most logical way to think about it. I would guess either this is, or there is a visual method.

anonymous · Answer

Okay, thank you! I very much appreciate it!