Question

The number of ways in which n distinct objects can be put into two different boxes so that no box remains empty, is

• A. $2^n-1$
• B. $n^2-1$
• C. $2^n-2$
• D. $n^2-2$

Answer 1

The correct option is C $2^n-2$

Each object can be put in $2$ ways (Box $1$ or Box $2$).

The number of ways in which object can be put in$=2\times 2\times 2\times ...2$ ($n$ times) $=2^n.$

Two of these choices correspond to either first or the second box is empty.

(i.e., Box $1=0$, Box $2=n$ and Box $1=n,$ Box $2=0$)

$\therefore$ Required number of ways $2^n-2.$