Question

{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?

Answer 1

Let the set $A$ consist of $n$ distinct elements and let $n\geq r$,

$a)$

When the elements in the sequence may be repeated, then we have $n^r$ sequences each of length $r.$

$b)$

When the elements in the sequence can not be repeated(distinct) then, there will be $^nP_r={n!\over (n-r)!}$ sequences each of length $r$.