First slide

Permutations

Question

If there are 62 onto mapping from a set X containing n elements to the set $Y = {- 1, 1}$ , then $n$ is equal to

Moderate

A

4
B

5
C

6
D

7

Solution

Let $X = \{x_{1}, x_{2}, \dots, x_{n}\}$
Each $x_{i}$ can have two images $v i z - 1$ and 1. Thus, there are $2^{n}$ mappings from $X$ to $Y$ .
But there are exactly two map ping which are not onto.
These are when all the elements are mapped to – 1 or when all the elements are mapped to 1.
$∴$ there are $2^{n} - 2$ onto mapping from $X$ to $Y$
$\begin{array}{ll} Set 2^{n} - 2 = 62 =\Rightarrow 2^{n} = 64 = 2^{6} \\ \Rightarrow n = 6 \end{array}$

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