HiAll,

Please help me in sorting my confusion

Question There are 5 green balls, 4 red balls and 6 blue balls
What is the probability of getting all three are different colour, when the three balls are picked one after the other without replacement

Answer

Method 1 :-Perms and comms way

Total ways of selecting 3 Balls one after the other is 15*14*13

No of ways of selecting 3 different colour balls are 5*4*6

Is it not 5*4*6 / 15 *14*13 ?

But in an article i saw it is (5*4*6 /15*14*13) *6
why a 6 is multiplied?

Method 2 :- Probability Way

But When i solve using probability approach I am getting a reason for 6

Probability of selecting Green ball without replacement is 5/15
Probability of selecting Red ball without replacement is 4/14
Probability of selecting blue ball without replacement is 6/13

hence for
Green , Red ,Blue it is 5/15 * 4/14 * 6/13
similarly it goes for various other 5 arrangement hence it 6 *(5/15 * 4/14 * 6/13).

Getting confused, which one is the right answer?