Permutations
and Combinations
When we talk of permutations
and combinations we often use the two terms
interchangeably.

In statistics, the two each have very specific meanings.
The permutation
of a number of objects is the number of different ways they can be
ordered: the position is important. With combinations, one
does not consider the order in which objects were placed.

This algorithm (program in Matlab) calculates the number of permutations and combinations
of N
objects taken D
at a time.
The full Matlab code is:
%
Clears
variables and screen
clear;
clc
%
Asks
user for input
n
= input('Total
number
of objects: ');
d = input('Size
of
subgroup: ');
%
Computes
and displays permut. according to basic formulas
p
= 1;
for
i = n  d + 1 :
n
p
= p*i;
end
str1
=
[num2str(p) '
permutations'];
disp(str1)
%
Computes
and displays combin. according to basic formulas
str2
=
[num2str(p/factorial(d)) '
combinations'];
disp(str2)
Example
1:
How many
permut. and combin. can be made of the 26 letters of the
alphabet, taking five at a time?
We run the
code above and enter:
Total number of objects: 26
Size of
subgroup: 5
The answer is:
7893600
permutations
65780
combinations
Example 2:
How many different ways can 12 computers be repaired if the workshop
can
only support 2 at a time?
We run the Matlab mfile above and enter:
Total
number of objects: 12
Size of
subgroup: 2
The answer (with no doubt) is:
132 permutations
66
combinations
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