solve for n in the permutation

Question

please help me im stuck and need help on this question. I have tried the equation n!/ (n-1)! and i could not get the right answer. please i need help

this is the question: n+1P3=12(n-1P2)

Answer 1

On the left, you have (n+1)P(3) = $(n+1)(n)(n-1)$ and on the right, you have (n-1)P(2) = $(n-1)(n-2)$. Then you have the equation:

$$(n+1)(n)(n-1)=12(n-1)(n-2)$$

$$(n+1)n=12(n-2)$$

$$n^2+n=12n-24$$

$$n^2-11n+24=0$$

$$(n-8)(n-3)=0$$

We find the solutions $n=3$ and $n=8$.