F. How many different sequences, each of length r, can be formed using elements from A if (a) elements in the sequence may be repeated? (b) all elements in the sequence must be distinct?

Let the set $A$ consistss from $n$ distinct elements, $n\geq r.$

(a)

$n^r$ sequences, each of length $r$ can be formed using elements from $A$ if elements in the sequence may be repeated.

(b)

$P(n, r)=\dfrac{n!}{(n-r)!}$ different sequences, each of length $r$ can be formed using elements from $A$ if all elements in the sequence must be distinct.