Answer:
n = 5
Step-by-step explanation:
nPr = n!/(n - r)!
nP3 = n!(n - 3)! = 60
n(n - 1)(n - 2)(n - 3)! / (n - 3)! = 60
n(n - 1)(n - 2) = 60
n³ - 3n² + 2n - 60 = 0
Try n - 5 as a factor.
(n³ - 3n² + 2n - 60)/(n - 5)
n² + 2n + 12
---------------------------------
n - 5 | n³ - 3n² + 2n - 60
n³ - 5n²
---------------------
2n² + 2n
2n² - 10n
--------------------------
12n - 60
12n - 60
----------------
0
n³ - 3n² + 2n - 60 = 0
(n - 5)(n² + 2n + 12) = 0
n - 5 = 0
n = 5
Answer: n = 5
