Hi, i need help solving for n
a) n!/(n-2)!=930
b) P(n,5)= 42 x P(n,3)
Thank you
Use the Identity that
$\displaystyle n!=n(n-1)!=n(n-1)(n-2)!$
This yeilds
$\displaystyle \frac{n(n-1)(n-2)!}{(n-2)!}=930$
Simplify from here and solve for n.
Hint: you will get quadratic equation and only keep the positive solution
Try something similar for the nextone. Use the Formula for $\displaystyle P(n,r)$
You can simplify by (n-1)(n-2) considering that 1 and 2 are not solutions of initial equation
(n-3)(n-4)=42
You can solve by using usual method of second degree equation or just looking at the equation
n-3 and n-4 are two consecutive integers
You surely know two consecutive integers whose product gives 42
One is equal to n-3 and the other one to n-4