Question

how many ways can five distinct antiques be divided among two brothers such that each get atleast one antique piece

Answer 1

In the following ratios:

A : B

A gets 1 antique, B gets 4 antiques

A gets 2 antiques: B gets 3 antiques

A gets 3 : B gets 2

A gets 4: B gets 1

SO there are 4 different ways.

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Answer 2

In this case since the values of the antiques are not mentioned it’s safe to assume that they are of equal value.

Now brother 1 can have four while brother 2 can have one.

Brother 1 can have three and brother 2 can have two.

Brother 1 can have two and brother 2 can have three.

Brother 1 can have one and brother 2 can have four.