The symbol $P(n, r)$ denotes the number of permutations of `n` objects taken `r` at a time. The symbol $P(n, r)$ denotes the number of permutations of `n` objects taken all at once. In our example, there are $6$ possible permutations of $3$ different objects. The permutation or shorter nPr is the number of ways in which we can choose `r (r\leq n)` different objects out of a set containing `n` different objects, where the order of the elements is important. For example, if we buy three different books in a different order, how many elements would the corresponding sample space have? Denoting them $1, 2,$ and $3,$ the sample space is The field of mathematics which studies different possibilities for the arrangement of objects is called combinatorics.
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