First slide

Combinations

Question

The number of ways in which $n$ distinct objects can be put into two different boxes, is

Moderate

A

$n^{2}$
B

$2^{n}$
C

$2 n$
D

none of these

Solution

Let the two boxes be $B_{1}$ and $B_{2}$ .There are two choices for each of the $n$ objects. So, the total number of ways is
$\frac{2 \times 2 \times \dots \times 2 = 2^{n}}{n - t i m e s}$

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