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  4. 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 qp Statement 2: The total number of selections of p different objects out of q objects is qCp.

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Q. 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 $^qC_p$.

AIEEEAIEEE 2012Permutations and Combinations

Solution:

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 $^qC_p$.
It is also a true statement and it is a correct explanation for statement -1 also.