Question

A____ is an arrangement of all or part of a set of objects in a definite order.

Answer 1

First we need to understand the difference between a permutation and a combination. A combination mainly gives attention to the selection part of objects without regard to the order in which they are selected. A permutation, instead, gives more attention to the arrangement part of objects with regard to the order in which they are arranged.

Complete step-by-step solution:
Generally, Statisticians use a specific terminology for permutations. They describe permutations as $n$distinct objects taken $r$at a time. Here, $n$ refers to the number of objects from which the permutation is formed, and $r$ refers to the number of objects used to form the permutation.
Now, we will take an example according to the previous paragraph. The permutation was formed from $3$ letters $(A,\,B,\,and\,C)$. So, $n = 3$, and the permutation consisted of $2$ letters, therefore, $r = 2$.
Therefore, the number of permutations of $n$ objects taken $r$ at a time is written as:
${{}^n}P_r = n(n - 1)(n - 2)...(n - r + 1) = \dfrac{{n!}}{{(n - r)!}}$
Therefore, A permutation is an arrangement of all or part of a set of objects in a definite order.

Note: We should keep in mind that the letters AB and BA represent two different permutations, because the order is different. So, we represent only 1 combination; because order is not important in a combination.