# Drawing balls without replacement

#### Jared Sy

##### New Member
Our teacher gave us this problem:

In how many ways can 3 balls be drawn from a bag of 12 balls for 4 consecutive times without replacement?

My solution was 12C3+9C3+6C3+3C3, but his solution was 12!/(3!*3!*3!*3!). He didn't explain why my solution was wrong though. But I really feel that I'm correct on this one

#### Dason

Can you explain your logic. Because I think you have one misunderstanding that when corrected would let you use your logic to get the right answer.

#### Dason

Hint: should you be really be *adding* here

#### Jared Sy

##### New Member
Well, because at first you have to draw 3 balls out of 12, then 3 out of 9 and so on. ... And I think I got your point, hahaha. Thank you!

#### Dason

Perfect. And that will give the same answer as the "correct" answer after reducing.

#### obh

##### Member
The simple logic behind your teacher's formula could be explained as follows: (which is the same logic to explain the C formula)

Out of the bag 12 balls were drawn, hence 12! different combinations

The order in each group of 3 balls doesn't matter in this problem: 3! combinations per group
divide by 3! per each group.
do it 4 times as you have 4 groups.

result: 12!/(3!*3!*3!*3!)