You are here:

Advanced Math/Maths -Permutation and combination

Advertisement

Expert: Sherry Wallin - 11/23/2010


Question

(n+3)!=110(n+1)!
Find the value of n ,where n! is n factorial  

Answer
Hi Dhananjay~
The interesting thing about factorials is that you can find immense cancellation. For example 5!/3! = 5*4*3!/3! = 5*4 = 20

In your problem (n+3)! = (n+3)(n+2)(n+1)!

so...

(n + 3)! = 110(n + 1)!  =>
(n + 3)(n + 2)(n + 1)! = 110(n + 1)!  =>
(n + 3)(n + 2) = 110  =>
n^2 + 5n + 6 = 110  =>
n^2 + 5n - 104 = 0  =>
(n + 13)(n - 8) = 0  =>
n + 13 = 0  or  n - 8 = 0  =>
n = -13 or n = 8

It can't be that n = -13 because factorials are NOT defined for negative numbers, thus the only solution is n = 8.

Math Prof

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

©2012 About.com, a part of The New York Times Company. All rights reserved.