Question

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?

Answer 1

Let the set $A$ consists 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.