Statistics Permutation – lesscss

By | November 29, 2018

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

${^nP_r = frac{n!}{(n-r)!} }$

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!}{(26-10)!} \[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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