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.

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!)