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(B) Statement-$1$: The number of functions from a set $A$ with $n(A) = p$ elements to a set $B$ with $n(B) = q$ elements is given by $q^p$. This is a

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Statement $1$ is true,Statement $2$ is true,Statement $2$ is not a correct explanation of Statement $1$.

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(B) Statement-$1$: The number of functions from a set $A$ with $n(A) = p$ elements to a set $B$ with $n(B) = q$ elements is given by $q^p$. This is a standard result in set theory. Thus,Statement-$1$ is true.Statement-$2$: The number of ways to select $p$ objects from $q$ distinct objects is given by the combination formula ${}^qC_p = \frac{q!}{p!(q-p)!}$. This is a true statement.However,Statement-$2$ describes the number of combinations,which is a fundamental counting principle,but it does not explain why the number of functions from $A$ to $B$ is $q^p$. The number of functions is derived from the fact that each of the $p$ elements in $A$ has $q$ choices in $B$. Therefore,Statement-$2$ is not the correct explanation for Statement-$1$.

Statement $1$ : If $A$ and $B$ are 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 ${}^qC_p$.

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Statement $1$ : If $A$ and $B$ are 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 ${}^qC_p$.