formula for permutation, combination and factorial?

Let's say we have 3 balls, red, blue and green

In how many ways can we select two balls?

Red, Green is one order, Green, Blue is another

So if order is important we got permutation and 6 possible ordered options

If order is not important then we get just three selections which is combination

If n is the number of things to choose from, and we choose, R, of them

Then formula is shown in the image

The factorial function is denoted with symbol exclamation, here we multiply all whole numbers from our chosen number down to 1

factorial of 1 is 1, factorial of 3 is 3 times, 2 times 1 or 6

in permutation without repetition, we have to reduce the number of available choices each time