Answer:
n = 19/6
Step-by-step explanation:
Formula for C(n,r) = n!/(r!(n-r)!)
C(n,3) = n! /( 3! * (n - 3)!)
Formula for P(n,r) = n!/(n-r)!
P(n,2)= n!/(n-2)!
C(n, 3) = P(n, 2)
n! /( 3! * (n - 3)!) = n!/(n-2)!
[tex]\frac{n!}{3!(n-3)!}= \frac{n!}{(n-2)!}[/tex] cross multiply
n!(n-2)! = n! 3! (n-3)!
(n-3)! = (n-3)(n-2)!
so n!(n-2)! = n! 3! (n-3)! becomes
n!(n-2)! = n! 3! (n-3)(n-2)! divide both sides by n!(n-2)!
1 =6(n-3)
1 =6n -18
19 = 6n
n = 19/6
