State fundamental counting principle and select what is the meaning of $P_{r}^{n}$ ?

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The number of permutations of ‘n’ different things, taking ‘r’ at a time

The number of combinations of ‘n’ similar things, taking ‘r’ at a different time

The number of permutations of ‘n’ equal things, taking ‘r’ at rate

None

answer is A.

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Detailed Solution

Fundamental principle counting is the base of counting which is comprised of addition as well as multiplication rules.
Here, multiplication principle says that where there are "m" types of methods to execute one operation, and "n" different ways to perform these operation one after, then the 2 operations can be finished in (m x n) different ways.
Here, we can add finite number of operations.
Also, by the Addition principle when there are "m" different methods to do single operation and "n" types of ways to perform another operation which are unrelated to the first one then, '(m + n)' operations can be found to do either of the 2 procedures.
Here, finite set of mutually exclusive operations can be included in this operation.
Now, the definition of