Question 773522
Nineteen identical ball bearings are to be randomly shared by two girls and three boys anyhow. In how many ways can the ball bearings be shared in such a way that the boys will receive one ball bearing each and the rest go to the girls? 
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Pick 3 for the boys: 19C3 ways
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That leaves 16 for the two girls.
One of the two girls may receive: 0,1,2,3....14,15 or 16 balls
The other girl will receive what's left over.
The girl distribution can be done is 2*17 = 34 ways
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Total # of ways: 19C3*34 = 32946 ways
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Cheers,
Stan H.
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