Expected Profit from a Lottery Ticket 
Ahmed is playing a lottery game where he must pick 2 numbers from 0 to
  9 and then one letter out of the 26-letter English alphabet. He may
  choose the same number both times. If his ticket matches the 2 numbers
  and 1 letter drawn in order, he wins the grand prize and receives
  \$10,405. 
If just his letter matches but one or both of his numbers do not
  match, he wins the small prize of \$100. Under any other outcome he
  loses and receives nothing. The game costs him \$5 to play. He has
  chosen the ticket 04R. Assuming that he paid the \$5 and he picked the
  ticket 04R.

The solution to the problem is found in this video: https://www.youtube.com/watch?v=6vlBOHckmzU&feature=youtu.be 
In the video, the probability of getting the small prize is (1/26) - (1/2600). Shouldn't the probability of winning the small prize be the sum of the probabilities of getting the letter right and 1 number wrong + getting the letter right and 2 numbers wrong: (1/26)(9/10)(1/10) + (1/26)(9/10)(9/10)?

Yes, but you are missing something. Can you figure it out?
$$2\cdot \frac{1}{26}\frac{1}{9}\frac{1}{10} +  \frac{1}{26}\frac{9}{10} \frac{9}{10} $$
