Question:
The total number of functions from the set A = (1, 2, 3, 4 to the set B = a, b, c) is _________.
Solution:
Given: $f: A \rightarrow B$ where $A=\{1,2,3,4\}$ and $B=\{a, b, c\}$
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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