i am asking a permutation question 16.nP3=n+lP3 what is the value of n?

Answer 1

QUESTION 16:

As far as I know there is no solution of n that will make nP3 = (n+1)P3.

The formula for nPr is:
n! / (n-r)!

With r = 3:
nP3 = n! / (n-3)!
(n+1)P3 = (n+1)! / (n+1 - 3)!

Equate these:
n! / (n-3)! = (n+1)! / (n+1 - 3)!

Now cross multiply:
n! (n-2)! = (n+1)!(n-3)!

On the left side factor out an (n-2) from the factorial:
(n-2)n!(n-3)! = (n+1)!(n-3)!

And on the right side factor out an (n+1) from the factorial:
(n-2)n!(n-3)! = (n+1)n!(n-3)!

If you remove the common n!(n-3)! from both sides you get:
n-2 = n+1

Then subtract n from both sides:
-2 = 1

The contradiction tells us that there is no solution.

Edit:

I just realized you are asking for 16 *times* nP3, not question #16.

16 * n(n-1)(n-2) = (n+1)(n)(n-1)

The n(n-1) cancels out:
16(n - 2) = (n + 1)

16n - 32 = n + 1
16n - n = 32 + 1
15n = 33
n = 33/15
n = 2 3/15
n = 2 1/5

Sorry about that... I got confused by your notation.

Answer 2

16P(n, 3) = P(n+1, 3)
Or 16n(n--1)(n--2) = (n+1)n(n--1)
Or 16(n--2) = n+1
Or 15n = 33
Or n = 33/15 = 2 1/5