Question

The total number of functions from the set A = (1, 2, 3, 4 to the set B = a, b, c) is _________.

Answer 1

Given: $f:A\to B\mathrm{where}A=\left\{1,2,3,4\right\}\mathrm{and}B=\left\{a,b,c\right\}$

Number of elements in A = 4
Number of elements in B = 3
Each element of A have 3 options to form an image.

Thus, Number of functions that can be formed = 3 × 3 × 3 × 3 = 81

​Hence, the total number of functions from the set A = {1, 2, 3, 4} to the set B = {a, b, c} is 81.

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