hsampath wrote:

Thanks hobbit. I came to my answer knowing I had missed something, but this is a great explanation.

I know you will probably frown upon doing it like this, would it be alright in all such cases to just divide by 12C3 (or equivalent ) in a problem without worrying about repetitions (or not)? I will also try to work this out shortly.

it is difficult to say what to do in "all such cases".... there is no rule for all cases. each question may contain a slightly different variant which may change the principle bes used to solve it....

it is important, though, to understand WHY 12C3 was used.

the denominator in probability calculations, usually represents the number of all possible cases. the numerator counts the relevant cases for the question. it is a MUST that the numerator and denominator count the same thing. it is like units of measurements in velocity. you cant just add velocities measured in MPH and mps, you need to convert.

12C3 counts the number of possibilities to choose 3 different items out of possible 12 different items, regardless of order.

12*11*10 counts the number of possibilities to choose 3 different items out of possible 12 different items with regard to order.

in this question if you count "green,yellow,white" and "yellow,white,green" as two different choices because of the order of draw - that's fine (this is how i did it). just count carefully, and divide by 12*11*10

if you count the possibility without regard to order, as ncprasad probably did (he just gave the formula, not explanation, so i'm not sure what went through his mind) - then divide by 12C3.

both ways are fine. just count carefully, and be aware what you are counting.