Question #98563
In how many ways can ball bearings labeled A, B, C and D be
shared by Jacob and Helen in such a way that
1 Jacob gets one ball bearing and Helen gets three
2 They each get two ball bearings?
1
Expert's answer
2019-11-13T11:38:24-0500

1


A+BCD,B+ACD,C+ABD,D+ABCA+BCD, B+ACD, C+ABD, D+ABC

Four ball bearings labeled A, B, C and D can be shared by Jacob and Helen in such a way that Jacob gets one ball bearing and Helen gets three in four ways.

2


AB+CD,AC+BD,AD+BC,AB+CD,AC+BD, AD+BC,BC+AD,BD+AC,CD+ABBC+AD, BD+AC,CD+AB


(42)=4!2!(42)!=4312=6\binom{4}{2}={4! \over 2!(4-2)!}={4\cdot3 \over 1\cdot2}=6

Four ball bearings labeled A, B, C and D can be shared by Jacob and Helen in such a way that Jacob gets two ball bearings and Helen gets two in six ways.


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