Question

1. Write in factorial form. n(n-1)(n-2)...(n-r+1)

Answer 1

The factorial form is given by

$n\mleft(n-1\mright)\mleft(n-2\mright)\ldots\mleft(n-r+1\mright)=\frac{n!}{(n-r)!}$

The above formula is true for (n ≥ r)

For example:

There are 3 ice-cream flavors and you have to choose 1

So that means n = 3 and r = 1

$\frac{n!}{(n-r)!}=\frac{3!}{(3-1)!}=\frac{3!}{2!}=\frac{3\times2\times1}{2\times1}=3$

This means that there are 3 different ways to choose 1 ice-cream flavor.

For example: