Question

Give Some Information on : pERMUTATION

Answer 1

what information? like when is it used?

Answer 2

Permutations
There are basically two types of permutation:

Repetition is Allowed: such as the lock above. It could be "333".
No Repetition: for example the first three people in a running race. You can't be first and second.

Answer 3

Permutations without Repetition

In this case, you have to reduce the number of available choices each time.


For example, what order could 16 pool balls be in?

After choosing, say, number "14" you can't choose it again.

So, your first choice would have 16 possibilites, and your next choice would then have 15 possibilities, then 14, 13, etc. And the total permutations would be:

16 × 15 × 14 × 13 × ... = 20,922,789,888,000

But maybe you don't want to choose them all, just 3 of them, so that would be only:

16 × 15 × 14 = 3,360

In other words, there are 3,360 different ways that 3 pool balls could be selected out of 16 balls.

But how do we write that mathematically? Answer: we use the "factorial function"

Answer 4

Permutations with Repetition

These are the easiest to calculate.

When you have n things to choose from ... you have n choices each time!

When choosing r of them, the permutations are:

n × n × ... (r times)

(In other words, there are n possibilities for the first choice, THEN there are n possibilites for the second choice, and so on, multplying each time.)

Which is easier to write down using an exponent of r:

n × n × ... (r times) = n^r

Example: in the lock above, there are 10 numbers to choose from (0,1,..9) and you choose 3 of them:
10 × 10 × ... (3 times) = 10^3 = 1,000 permutations
So, the formula is simply:

n^r
where n is the number of things to choose from, and you choose r of them
(Repetition allowed, order matters)