simplify n!/2!(n-2)!

then convert it to the form of n^{2 }+ bn + c = 0

Been stuck on this question for days!!!!

The full question is:

One model of boat has *n *optional features available. When 2 optional features are chosen for this model of boat, 45 packages are available. The number of optional features, *n*, available for this model of boat can be determined using the following expression: n! / 2!(n - 2)! = 45 n > 2

Simplify this expression, and write the answer in the form n^{2 }+ bn + c = 0. Please show all work.

Guest May 19, 2020

edited by
Guest
May 19, 2020

edited by Guest May 19, 2020

edited by Guest May 19, 2020

edited by Guest May 19, 2020

edited by Guest May 19, 2020

#1**+1 **

n! (n) ( n - 1)

_________ = __________ = (1/2) ( n ) ( n - 1) = (1/2) (n^2 - n)

(n - 2)! 2! 2

So.....I guess you want to set this to 0 ???

(1/2) ( n^2 - n) = 0 multiply both sides by 2

n^2 - n = 0

CPhill May 19, 2020

#2**0 **

The full question is as followed:

One model of boat has *n *optional features available. When 2 optional features are chosen for this model of boat, 45 packages are available. The number of optional features, *n*, available for this model can be determined using the following expression: n!

------------------ = 45 n > 2

2! (n - 2)!

Simplify this expression, and writhe your answer in the form n^{2 }+ bn + c = 0. Show all work.

Guest May 19, 2020