SOLUTION: Hi! I would like to ask some help regarding this question, where I need to find n. nP4 = 28 {(n - 1)P2)} I tried trial and error but it looks like it's a big number, it wo

Algebra ->  Permutations -> SOLUTION: Hi! I would like to ask some help regarding this question, where I need to find n. nP4 = 28 {(n - 1)P2)} I tried trial and error but it looks like it's a big number, it wo      Log On


   

Question 1179318: Hi! I would like to ask some help regarding this question, where I need to find n.
nP4 = 28 {(n - 1)P2)}
I tried trial and error but it looks like it's a big number, it would really mean a lot if you help me. Thank you!
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

    nP4     =  n*(n-1)*(n-2)*(n-3).


    (n-1)P2 =  (n-1)*(n-2).


Therefore, your equation is


    n*(n-1)*(n-2)*(n-3) = 28(n-1)*(n-2),   assuming  n >= 4.


Cancel the factors  (n-1)  and  (n-2)  in both sides


    n*(n-3) = 28.


You can solve it formally as a quadratic equation, or can guess the solution mentally in two seconds:  n = 7.


ANSWER.   n = 7.

Solved.