Suppose there are three piles of marbles coloured red,green and blue, with at least 20 marbles in each pile.In how many ways can 20 marbles be chosen if there must be at least 2red,at least 3green,and at least 4blue marbles?
Do you know the formula for the number of ways to put K identical objects into N different cells: Combin(K+N-1,K)=Combin(K+N-1,N-1).Originally Posted by dcapdogg
If we were to select any twenty balls from the piles without restriction, the number of possible selections is the number of non-negative integer solutions to R+G+B=20.
That how many ways can we put twenty ones into three difference places? For example: R=6, G=9 & B=5; R=0, G=7 & B=13. From the above the answer is Combin(20+3-1,20)=Combin(22,2).
Now, how can we answer your question? We need R to be at least 2, G to be at least 3 and B to be at least 4. So using the 20, just go ahead and put 2 into the R cell, 3 into the G cell and 4 into the B cell. Thus we have 11 left to put into any of the three cells. How many ways can that be done?