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

1 Answer
Parabola
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 6Pr=30, we have: (6!)/((6-r)!)=30=>720/((6-r)!)=30/1
Using the fact that (a*b)/(c*b)=a/c, we can see that:
720/((6-r)!)=30/1
(720*x)/((6-r)!*x)=30/1
Where x=30/720=>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

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