Question

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

Answer 1

`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`