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 ${}^q{C}_p$.

• A. Statement 1 is true. Statement 2 is false.
• B. Statement 1 is true. Statement 2 is true. Statement 2 is not a correct explanation of Statement 1.
• C. Statement 1 is false, Statement 2 is true
• D. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

Answer 1

Answer: (D)

Statement -1 : $n(A)=p,n(B)=q,q>p$ Total number of functions from $A\to B=q^p$ It is a true statement.
Statement - 2 : The total number of selections 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.