Question

An art gallery has 8 new paintings, all the same size, but enough room on the wall for only 6 of them.

How many ways can the director arrange the 8 paintings on the wall?

A. 40,320
B. 48
C. 20,160
D. 28

Answer 1

@jigglypuff314

Answer 2

I think it might be 8*7*6*5*4*3 = ?

Answer 3

Idk... why did you also multiply 5! - ?
They don't mention any numbers under 6

Answer 4

8*7*6*5*4*3
^ ^ ^ ^ ^ ^ 6 numbers
counting down from 8 because once you put a picture up, you have one less to choose from each time

Answer 5

I see... well, now it makes sense.
But I just don't get why it wouldn't be 8*6 or something else

Answer 6

idk why too xD
I just saw sourwig help before and to the problem like that... idk much else, sorry

Answer 7

Oh, it's alright :)
Speaking of sourwing, I wanna show you something, just a sec

Answer 8

48

Answer 9

The way you can select 6 things from 8 things is
8! / 6!*(8-6)! = 28
So there are 28 ways in which 6 paintings may be chosen from 8.
Each of those 28 can be arranged in 6*5*4*3*2 (720) ways.
So the total number of arrangements is 28 * 720
20,160
answer is C

Answer 10

so I was right, ok, thank you! :)

Answer 11

Provided we both are right

Answer 12

Alright, thank you both :)