Question

because all permutation problems are also fundamental counting​ problems, they can be solved using the formula for or using the fundamental counting principle.

Answer 1

The Statement that "Because all permutation problems are also Fundamental Counting problems, they can be solved using the formula for nPr or using the Fundamental Counting Principle." is True.

As per the question-statement, all permutation problems are also Fundamental Counting problems and they can be solved using the formula for nPr or using the Fundamental Counting Principle.

We will have to find out the truthfulness of this above-mentioned statement.

First of all, permutations are each of several possible ways in which a set or number of things can be ordered or arranged, and thus, the first part of our statement is true that, all permutation problems are also Fundamental Counting problems.

Now, the nPr Formula goes as $\frac{n!}{(n-r)!}$ which itself is based on the fundamental counting principle, and any Fundamental Counting problem can be solved using the fundamental counting principle. Therefore, the second part of our statement is also true that, all permutation problems  can be solved using the formula for nPr or using the Fundamental Counting Principle.

• Permutation: Each of several possible ways in which a set or number of things can be ordered or arranged and can be calculated by the formula $nPr = \frac{n!}{(n-r)!}$.

• Fundamental Counting Principle: The Fundamental Counting Principle states that if an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is (m × n).

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