Statistics – Permutation
A permutation is an arrangement of all or part of a set of
objects, with regard to the order of the arrangement. For
example, suppose we have a set of three letters: A, B, and C. we
might ask how many ways we can arrange 2 letters from that set.
Permutation is defined and given by the following function:
Formula
${^nP_r = frac{n!}{(nr)!} }$
Where −

${n}$ = of the set from which elements are permuted.

${r}$ = size of each permutation.

${n,r}$ are non negative integers.
Example
Problem Statement:
A computer scientist is trying to discover the keyword for a
financial account. If the keyword consists only of 10 lower case
characters (e.g., 10 characters from among the set: a, b, c… w,
x, y, z) and no character can be repeated, how many different
unique arrangements of characters exist?
Solution:
Step 1: Determine whether the question pertains to permutations
or combinations. Since changing the order of the potential
keywords (e.g., ajk vs. kja) would create a new possibility, this
is a permutations problem.
Step 2: Determine n and r
n = 26 since the computer scientist is choosing from 26
possibilities (e.g., a, b, c… x, y, z).
r = 10 since the computer scientist is choosing 10 characters.
Step 2: Apply the formula
${^{26}P_{10} = frac{26!}{(2610)!} \[7pt] =
frac{26!}{16!} \[7pt] =
frac{26(25)(24)…(11)(10)(9)…(1)}{(16)(15)…(1)} \[7pt]
= 26(25)(24)…(17) \[7pt] = 19275223968000 }$
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