Question:
The total number of one-one functions from the set A = {a, b, c} to the set B = {x, y, z, t} is _________.
Solution:
Given: $f: A \rightarrow B$ where $A=\{a, b, c\}$ and $B=\{x, y, z, t\}$
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.