Lesson Permutations and Combinations

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Permutations are used to find the many different ways for an outcome to occur. In permuations, order does matter.

The formula should look like this:
{{{ P(n,r)= n!/(n-r)! }}}

Where ! is factorial, and n should always be bigger than r.

For example, let us say you have 4 swimmers, but you can only select 1 of them to swim at the big competition for the first round and another 1 to swim for the second round. How many different pairs can you have?

{{{ P(4,2) =  4!/(4-2)!  =  4!/2!  =  12 }}}

The result is that there are 12 different pairs of swimmers you can pick to swim at the competition.

Another Permutation are repetition ones. These can involve letter problems:

Use the equation: s!/(p!q!r!.........) Where s is the sum and p,q,r, and so on are the repeating letters.

How many different ways can you arrange {{{ banana }}}

6!/(3!2!) = 60

There are sixty different ways to arrange banana.

Combinations, on the other hand, is almost the same. This way, you find the possible outcomes of an event with the exception that order doesn't matter.

The formula should look like this:
{{{ C(n,r) = n!/(n-r)!r! }}}

For example, let us say you had a group of 5 students. Only 3 of them would present their project. How many different sets of three can you have?

{{{ C(5,3) = 5!/(5-3)!3! = 5!/2!3! = 10 }}}

The result is that there are 10 different sets of three of students that will present the group of five's project.