# Solving Permutations and Combinations.Solving for variable.Find the value of r in 6Pr = 30?

Jan 18, 2018

$r = 2$

#### Explanation:

For this problem, I will use the simplest way possible to solve this.
Remember that: nPr=(n!)/((n-r)!)

For $6 P r = 30$, we have: (6!)/((6-r)!)=30=>720/((6-r)!)=30/1
Using the fact that $\frac{a \cdot b}{c \cdot b} = \frac{a}{c}$, we can see that:
720/((6-r)!)=30/1
(720*x)/((6-r)!*x)=30/1
Where $x = \frac{30}{720} \implies \frac{1}{24}$

Therefore,
(720*1/24)/((6-r)!*1/24)=30/1
Which means that (6-r)!*1/24=1. We try to simplify this equation.
(6-r)! =24
Now, we try to think of our basic factorial numbers.
1! =1
2! =2
3! =6
4! =24
Oh! $6 - r$ must equal 4...!

We can now solve the equation:
$6 - r = 4$
$- r = - 2$
$r = 2$