First slide

Permutations

Question

Let S be the set of all functions from the set A to the set A. If n(A) = k then n(S) is

Moderate

A

k!
B

k^k
C

2^k – 1
D

2^k

Solution

Each element of the set A can be given the image in the set A in k ways.
$∴$ the required number of functions, i.e.,
$n (S) = k \times k \times \dots (k times) = k^{k}$ .

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