Solve the following equation for n C (n+1, 3) = C(n,2) I know the answer is 5 - since I did trial and error, but how would I show the work?

You'll solve this equation involving combinations using
the factorial formula for combinations of n elements taken k at a
time:

C(n,k) = n!/k!(n -
k)!

Let's evaluate C(n+1 , 3) = (n+1)!/3!(n+1-3)! =
(n+1)!/3!(n - 2)!

Let's evaluate C(n , 2) =
n!/2!(n-2)!

Now, we'll equate the equivalent
expressions:

(n+1)!/3!(n - 2)! =
n!/2!(n-2)!

We'll simplify both sides by
(n-2)!

(n+1)!/3! = n!/2!

We
can write (n+1)! = n!*(n+1)

We can write 3! =
2!*3

n!*(n+1)/2!*3 =
n!/2!

We'll simplify both sides by
n!/2!:

(n+1)/3 = 1

We'll cross
multiply:

n + 1 = 3

n = 3 -
1

n = 2

Since
the value of "n" has to be a natural number, therefore a positive integer, we'll accept
n=2 as solution of the given equation.