SOLUTION: A child removes the name cards on ten wrapped christmas presents of which 6 are for the Phillps and 4 are for the Wongs. If the presents are distributed to the 2 families without r

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Question 769797: A child removes the name cards on ten wrapped christmas presents of which 6 are for the Phillps and 4 are for the Wongs. If the presents are distributed to the 2 families without reopening the packages, what is the expected number of correct presents distributed to the Phllips? Please show the work to get to the answer.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

There are 10 presents, so there are C(10,6) = 210 combinations
of 6 presents which could have gone to the Phillips 

   Delivered to     |           Number             |           |
X|    Phillips      !           of ways            |    P(X)   |  X*P(X)          
------------------------------------------------------------------------
6 correct           |   C(6,6) = 1                 |    1/210  |   6/210  
5 correct, (1 wrong)|   C(6,5)*C(4,1) =  6*4 = 24  |   24/210  | 120/210 
4 correct, (2 wrong)|   C(6,4)*C(4,2) = 15*6 = 90  |   90/210  | 360/210   
3 correct, (3 wrong)|   C(6,3)*C(4,3) = 20*4 = 80  |   80/210  | 240/310   
2 correct, (4 wrong)|   C(6,2)*C(4,4) = 15*1 = 15  |   15/210  |  30/210 
------------------------------------------------------------------------
                                              E(x) = ∑(X*P(X)) = 756/210 = 3.6

Edwin