Answer:
The number of plates that can be made without repetition is 3124550.
Step-by-step explanation:
The appropriate way to determine the number of plates to be made is by the application of combination.
Since the digits has 9 elements and the letters have 26, then 26[tex]C_{9}[/tex].
So that:
n[tex]C_{r}[/tex] = [tex]\frac{n!}{(n - r)!r!}[/tex]
n = 26 and r = 9;
26[tex]C_{9}[/tex] = [tex]\frac{26!}{(26 - 9)9!}[/tex]
= [tex]\frac{26!}{17!9!}[/tex]
= [tex]\frac{26*25*24*23*22*21*20*19*18*17!}{9*8*7*6*5*4*3*2*1*17!}[/tex]
= [tex]\frac{1.133836704*10^{12} }{362880}[/tex]
= 3124550
The number of plates that can be made without repeating numbers and letters is 3124550.
