Q. Let $A$ be a set containing 10 distinct elements, then the total number of distinct function from $A$ to $A$ is
A) $10^{10}$
B) 101
C) $2^{10}$
D) $2^{10} - 1$
Explanation
(a)
Given a set containing 10 distinct elements and $f:A \rightarrow A$ Now, every element of a set $A$ can make image in 10 ways.
$\therefore$ Total number of ways in which each element make images $= 10^{10}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.