In the province of Saskatchewan in Canada where I live our plates have three digits followed by three letters. (eg. 365 SYT) Hence there are 10 choices for each digit giving 10 10 10 = 1000 possible three digit numbers. There are 26 letters in the alphabet so there are 26 26 26 = 17576 possible 3 letter "words". Since any three digit number can go with any three digit "word" there are 17576 1000 = 17,576,000 possible plates. This is not actually true since there are some restrictions. A three letter "word" that is an english word isn't allowed and also some well known three letter acronyms are not allowed.
Can you now answer your question about the number of possible plated in New York?