evaluate the expression ₆ P ₀ I am not sure how to do this problem can some one show me how to do this step by step
By definition
nPr = n!/(n-r)!
so 6P0
= 6! / (6-0)!
= 6!/6!
= 1
If you have a scientific calculator, look to see if you have a key that looks like nPr
on mine to do something like 6P2
I would enter the following key strokes
6
2nd nPr
2
=
to get 30
Notice 6P2
= 6!/4!
= 6x5x4! /4!
= 6x5
= 30
To evaluate the expression ₆P₀, you need to understand the concept of permutations. Permutations, denoted as nPm, represent the number of ways to arrange or select m elements from a set of n elements without repetition.
In this case, ₆P₀ means selecting 0 elements from a set of 6 elements. When you select 0 elements, it means that you are not selecting anything.
The formula for permutations is given by:
nPm = n! / (n - m)!
However, when m is 0, (n - m)! becomes (n - 0)! which simplifies to n!.
So, for ₆P₀:
6! / (6 - 0)!
6! / 6!
= 6 x 5 x 4 x 3 x 2 x 1 / (6 x 5 x 4 x 3 x 2 x 1)
= 1
Therefore, ₆P₀ equals 1.