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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 ${}^q{C_p}$.
Statement $1$ is true, Statement $2$ is false
Statement $1$ is true, Statement $2$ is true,Statement $2$ is not a correct explanation of Statement $1$
Statement $1$ is false, Statement $2$ is true
Statement $1$ is true, Statement $2$ is true,Statement $2$ is a correct explanation of Statement $1$
Solution
statement-$1$ : $n\left( A \right) = p,n\left( B \right) = q,q > p$
Total number of funtions from $A \to B = {q^p}$
It is a true statement.
Statement-$2$ : The total number of selection of $p$ different objects out of $q$ objects is $^q{C_p}$.
It is also a true statement and it is a correct explanation for statement- $1$ also.
