Question

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

Answer 1

Hint: 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.