A state is considering license plates that have two digits followed by four letters. Assuming no combinations are excluded, how many different plates are possible if no repetitions of letters or digits are allowed?

Accepted Solution

Answer:32,292,000Step-by-step explanation:In your question, it asks how many license plate combinations we could make WITHOUT repeats.We need some prior knowledge to answer this question.We know that:There are 26 letters in the alphabetWe can make 10 digits (0 - 9)With the information we know above, we can solve the question.Since we CAN'T have repeats, we would be excluding a letter or number for each license plate.We're going to need to multiply each "section" in order to find how many combinations of license plates we can make.We decrease by one letter and one number in each section since we can't have repeats.Now, we can solve.Work:[tex]26*25*24*23*10*9 = 32,292,000[/tex]When you're done multiplying, you should get 32,292,000.This means that there could be 32,292,000 different combinations of license plates.I hope this helps you out.Good luck on your academics.Have a fantastic day!