Question

The total number of one-one functions from the set A = {a, b, c} to the set B = {x, y, z, t} is _________.

Answer 1

Given: $f:A\to B\mathrm{where}A=\left\{a,b,c\right\}\mathrm{and}B=\left\{x,y,z,t\right\}$

Number of elements in A = 3
Number of elements in B = 4

To form a one-one function,

Element a ∈ A have 4 options to form an image.
Element b ∈ A have 3 options to form an image.
Element c ∈ A have 2 options to form an image.

Thus, Number of one-one functions that can be formed = 4 × 3 × 2 = 24

​Hence, the total number of one-one functions from the set A = {a, b, c} to the set B = {x, y, z, t} is 24.

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