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Question

In how ways can $$5$$ different things be divided between $$A$$ and $$B$$ so that each receive at least one thing is


A
30
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B
60
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C
20
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D
80
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Solution

The correct option is A $$30$$
There $$5$$ different things and both $$A$$ and $$B$$ have to get at least one.
So we can given $$A$$, $$4$$ items in $$^5C_4$$ ways and remaining $$1$$ to $$B$$ in $$1$$ way. Similarly we can give $$A$$, $$3$$ items in $$^5C_3$$ ways and remaining $$2$$ items to $$B$$ in $$1$$ way.
Hence, required number of ways $$=^5C_1+^5C_2+^5C_3+^5C_4 =30 $$

Mathematics

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