Before we discuss permutations we are going to have check at what the words combination means and permutation. A Waldorf salad may be a mixture of among other things celeriac, walnuts and lettuce. It doesn’t matter in what order we add our ingredients but if we’ve a mixture to our padlock that’s 4-5-6 then the order is extremely important.

If the order doesn’t matter then we’ve a mixture , if the order do matter then we’ve a permutation. One could say that a permutation is an ordered combination.

The number of permutations of n objects taken r at a time is decided by the subsequent formula:

P(n,r)=n!(n−r)!

n! is read n factorial and means all numbers from 1 to n multiplied e.g.

5!=5⋅4⋅3⋅2⋅1

This is read five factorial. 0! Is defined as 1.

0!=1

Example

A code have 4 digits during a specific order, the digits are between 0-9. what percentage different permutations are there if one digit may only be used once?

A four digit code might be anything between 0000 to 9999, hence there are 10,000 combinations if every digit might be used quite just one occasion but since we are told within the question that one digit only could also be used once it limits our number of combinations. so as to work out the right number of permutations we simply connect our values into our formula:

P(n,r)=10!(10−4)!=10⋅9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅16⋅5⋅4⋅3⋅2⋅1=5040

In our example the order of the digits were important, if the order didn’t matter we might have what’s the definition of a mixture . the amount of combinations of n objects taken r at a time is decided by the subsequent formula:

C(n,r)=n!(n−r)!r!