Question

evaluate the factorial expression (n-4)!/n+4

Answer 1

Answer:

Evaluations shown below

Step-by-step explanation:

Factorial of a Number

Given a non-negative integer number n, we define its factorial n! as the product of every integer from 1 to n in steps of 1. For example

5!=5*4*3*2*1=120

It's defined that 0!=1

We are required to evaluate the factorial expression (n-4)!/n+4. We are not given specific values of n, so we'll pick up some of them. Note that n-4 must be non-negative, so n must be greater or equal to 4.

For n=7

(7-4)!/7+4=3!/7+4=6/7+4=34/7

For n=8

(8-4)!/8+4=4!/8+4=24/8+4=7

For n=10

(10-4)!/10+4=6!/10+4=720/10+4=76

Answer 2

Answer:

$\frac{(n+4)!}{(n+4)}=(n+3)!$

Step-by-step explanation:  

The correct question is

Evaluate the factorial expression $\frac{(n+4)!}{(n+4)}$

we know that            

The n! is defined as              

$n!=n(n-1)!$                                      

so                                                    

$(n+4)!=(n+4)(n+4-1)!=(n+4)(n+3)!$                      

substitute in the given expression                              

$\frac{(n+4)(n+3)!}{(n+4)}$                                                                    

Simplify (n+4)                                                                      

$\frac{(n+4)(n+3)!}{(n+4)}=(n+3)!$                        

therefore                                                                                                            

$\frac{(n+4)!}{(n+4)}=(n+3)!$