**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?**

The **Answer to the Question**

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**Here's the Solution to this Question**

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.