Question

Bicycle license plates in Flatville each contain three letters. The first is chosen from the set ({C,H,L,P,R}) the second from (A,I,O), and the third from ({D,M,N,T}). When Flatville needed more license plates, they added two new letters. The new letters may both be added to one set or one letter may be added to one set and one to another set. What is the largest possible number of ADDITIONAL license plates than can be made by adding two letters?

Answer 1

$5\cdot3\cdot4=60$ - the current possible number of plates

after adding 2 letters into the 1st set:
$7\cdot3\cdot4=82$
after adding 2 letters into the 2nd set:
$5\cdot5\cdot4=100$
after adding 2 letters into the 3rd set:
$5\cdot3\cdot6=90$
after adding 1 letter into the 1st set and 1 into the 2nd set:
$6\cdot4\cdot4=96$
after adding 1 letter into the 1st set and 1 into the 3rd set:
$6\cdot3\cdot5=90$
after adding 1 letter into the 2nd set and 1 into the 3rd set:
$5\cdot4\cdot4=80$

The largest possible number of plates after adding two numbers is 100.
So, the largest possible number of additional plates is 100-60=40