a) Tom chose any 4 of 6 places for the A's and for each of these, he chose any of 26 letters for the final two places
b ) Tom's answer is wrong because he forgot to break the problem down into cases.....the answer should be smaller (we will prove this in a sec ).....his answer = 10140 plates
c ) At least 4 As means 4As, 5As or 6As
4As = C(6,4) (25)^2 choose any 4 positions for the As and choose any of 25 letters for the other two positions
5As = C(6,5) ( 25) Choose any 5 of 6 positions for the As and we can use any of twenty five letters in the remaining position
6As = obviously only one way for this to occur
C(6,4)(25)^2 + C(6,5)(25) + 1 =
9526 plates