Subject: permutations and combinations
Name: Naomi
Who are you: Student

The state of New York has licence plates with five numbers followed by either a letter A or a letter B (eg. 36457A ,59972B ). How many licence plates are possible ?


Hi Naomi,

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 x 10 x 10 = 1000 possible three digit numbers. There are 26 letters in the alphabet so there are 26 x 26 x 26 = 17576 possible 3 letter "words". Since any three digit number can go with any three digit "word" there are 17576 x 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?