Picking r objects from n when order does NOT count

Question

In how many different ways can you grab three coins from a box containing 12 coins?

Answer 1

the formula for a combination is  n!/r!(n-r)!

12!/3!(12-3)!

12!/3!(9!)=12*11*10*9*8*.../(3*2*1)(9*8*...)

                 =12*11*10/3*2*1

                 =1320/6

                 =220

Answer 2

When order does not count, use combination.

There are 12C3 = 5184 different ways.

Answer 3

Hi Again Chris;

Another great question.

 

first   second   third

 

If there is NO replacement...

12x11x10=1320

 

If there is replacement...

12x12x12=1728