Question
In a certain state, license plates consist of three lettersfollowed by three numbers. a) How many different license plates can be made? b) How many different license plates can be made inwhich no letter or number appears more than once? c) A license plate is chosen at random. What isthe probability that no letter or number appears more thanonce? In a certain state, license plates consist of three lettersfollowed by three numbers. a) How many different license plates can be made? b) How many different license plates can be made inwhich no letter or number appears more than once? c) A license plate is chosen at random. What isthe probability that no letter or number appears more thanonce?
Explanation / Answer
There are 26 letters, and 10 possible numbers to choosefrom a) (26)(26)(26)(10)(10)(10) =263103=17,576,000 b) (26)(25)(24)(10)(9)(8) = 11,232,000 Since letters/numbers cannot be repeated, once you use aletter/number, you have less choice to choose from c)11232000/17576000 = 0.639 Part c is from basic probability, where you divide the totaldesired events by the total amount of events possible