Statement 1: If A and B be two sets having p and q elements respectively, where qp.

Question

Statement 1: If $A$ and $B$ be two sets having $p$ and $q$ elements respectively, where $q>p$. Then the total number of functions from set $A$ to set $B$ is $q^p$.

Statement 2: The total number of selections of $p$ different objects out of $q$ objects is $^qC_p$.

Accepted Answer

Statement 1 is true: each of the $p$ elements of $A$ can map independently to any of $q$ elements of $B$, giving $q^p$ functions.

Statement 2 is also true, and correctly explains the reasoning behind counting used implicitly. Both statements are true and consistent, and Statement 2 supports Statement 1's counting logic.

Solutions · 1