tarek99 wrote:

thanks guys. but i have a question. what are you logically doing when you multiply 6 by 3!? i don't understand the exact function of the 3! sometimes i see people divide the final number by a factorial and then sometimes i see people multiply. what are we logically doing when we do that? can someone explain?

The logic here is that, basically, we have 3 chairs where we should put 3 apples (A, B or C). What is the number of such combinations?

1st place: we could put any of 3 apples (A or B or C). We put A (but we could place B or C <-- order does not matter)

2nd place: we left with 2 apples (B or C) - so we put B (but we could put C)

3rd place - we left with only 1 apple

ABC

ACB

BAC

BCB

CAB

CBA

Total number of combinations is 3 * 2 * 1 = 3! = 6

But factorial is easy, try to place 4 apples on for chairs. Hope this helps.

P.S> If order matters, i.e. we need apple A on the first chair, the number of combinations would be: 1(A) * 2 (B or C) * 1 (the one that left after B or C)