SOLUTION: Eight plates are stacked in three piles with two piles of three plates each and one pile of two plates. You are to pick up the plates one at a time following these rules: 1) You

Algebra ->  Permutations -> SOLUTION: Eight plates are stacked in three piles with two piles of three plates each and one pile of two plates. You are to pick up the plates one at a time following these rules: 1) You       Log On


   

Question 927516: Eight plates are stacked in three piles with two piles of three plates each and one pile of
two plates. You are to pick up the plates one at a time following these rules:
1) You first choose a pile from which to pick up a plate.
2) You must then pick up the top plate from that pile.
By following these rules, in how many different orders can you pick up the eight plates?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the 1st pile of 3 plates.
Let B be the 2nd pile of 3 plates.  
Let C be the pile with 2 plates.

Each time you pick up all 8 plates can be represented by 
a seqeunce of 8 which contains 3 A's, 3 B's and 2 C's,

For instance, the sequence of 8: 

B,C,A,C,B,A,B,A represents the case where we pick up a plate from
pile B, then a plate from pile C, then one from A, C, and so
on until the 8th plate is picked from pile A.

In each such sequence there are C(8,3) positions for the 3 A's
to go.

That leaves 5 remaining positions for the B's to go.  So there
are then C(5,3) to choose positions for the B's to go.  Then the
remaining 2 are where the C's go.

Answer: C(8,3)C(5,3)C(2,2) = 56*10*1 = 560 ways to pick up
all the plates.

Edwin