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

1 Answer
Jan 18, 2018

Answer:

#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#