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

Question:

The total number of one-one functions from the set A = {a, bc} to the set B = {xyzt} is _________.

Solution:

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

Number of elements in = 3
Number of elements in = 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, bc} to the set B = {xyzt} is 24.