Question

completely stuck on homework -
A boat shop is promoting a particular model of boat that has various optional features. Each optional feature can be purchased separately. 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 your answer in the form n2 + bn + c = 0.

Answer 1

\[\frac{ n! }{ (2!)[(n - 2)!] } = 45 = \frac{ n(n - 1)(n - 2) . . .(3)(2)(1) }{ (2)[(n - 2)(n - 3)(n - 4) . . . (3)(2)(1)] } = \frac{ n(n-1) }{ 2 }\]
\[n ^{2} - n - 90 = 0 = (n + 9)(n - 10)\]
n = 10