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. $80$

Answer 1

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 ${}^5{C}_4$ ways and remaining $1$ to $B$ in $1$ way. Similarly we can give $A$, $3$ items in ${}^5{C}_3$ ways and remaining $2$ items to $B$ in $1$ way.
Hence, required number of ways ${=}^5{C}_1{+}^5{C}_2{+}^5{C}_3{+}^5{C}_4=30$