Solving permutation equations?

Question

How would you solve nP6 = 5*(nP5)?

I got to n!/(n-6)! = 5(n!)/(n-5)!, but I don't know how to cancel out the factorials. Please help

Answer 1

Not clear for me how the problem started, but I suppose you want to solve the equation

n!/(n-6)! = 5(n!)/(n-5)!

It is easy:

n!/(n-6)! = 5(n!)/(n-5)!

1/(n-6)! = 5/(n-5)!

(n-5)! = 5 (n-6)!

(n-6)! (n-5) = 5 (n-6)!

(n-5) = 5

n = 10

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Answer 2

First, cancel the n! from the two aspects: (n - 5)! = 5 * (n - 6)! Now, bear in recommendations how (n+one million)! = (n+one million) * n! properly, you ought to use comparable reasoning to verify that (n-5)! = (n-5) * (n-6)! replace that for the time of the left hand element: (n-5) * (n-6)! = 5 * (n-6)! Cancel out the (n-6)! area: n - 5 = 5 n = 10 verify to truly understand those identities, and notice that they make solid sense: (n+one million)! = n! * (n+one million) (n+one million)! / n! = n + one million you additionally could make different comparable equalities with 2 aspects: (n+2)! = (n+2)(n+one million) * n! merely write out the ! area longhand, and you will see how those paintings, and you would be waiting to be conscious them to stuff like changing (n-5)! into an expression regarding (n-6)!.