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
B
60
C
20
D
80

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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