Counting Homework

Question

Amber has ten paintings and have room to display only three of them at a time on her wall. How many different ways could she do this?

 ways.

Answer 1

you have 10 paintings to be displayed 3 at a time.

the number of ways that they can be displayed is 10C3 = 10! / (3!)(7!)

that means (10 X 9 X 8) / (3 X 2) = 120.

so there are 120 ways to display the paintings.

Answer 2

10P3 =10!/(10-3)! =10!/7!=720 ways

nPr=n!/(n-r)!, n=10, r=3

10!/7! = 10x9x8x7!/7!= 10x9x8 = 720

if order matters use the Permutation formula

for 10 objects taken 3 at a time

order matters means paintings displayed ABC, is a different way from BCA

if order doesn't matter, use the Combination formula

nCr = n!/(n-r)(r)! = 720/3x2 = 120 ways

combination means ABC is 1 way but BCA is not another way,both just 1 way

depending on how the problem is worded, its context

either might be right, 120 or 720