Question

1. A license plate must be 7 characters long; available characters are uppercase letters (26 possible letters for each spot), digits (0-9, so 10 possible numbers for each spot), and special characters!*-& and a blank space (5 possible special characters) A rental car company wants all of its cars' license plates to begin with 4 letters, then have 1 special character, and then 2 digits, e.g. "ABCD 68" is permissible, but " ABCD6 8" is not. (a) How many different license plates are possible for a car belonging to this company? b) How many different license plates are possible for a car in this company if none of the digits may be repeated? c) How many license plates are possible for a car in this company if no character (letters, special characters, or digits) can appear twice? (d) You rent a car from this company during an island vacation, but two days into your vacation the car is stolen. You need to file a police report, but you need to know the license plate of the car. You don't rmber the whole license plate, but you do remember that the first four characters are, aptly, "FRIG," n that order Because you just want to get back to sipping daiquiris on the beach, you decide to just take a random guess at the remaining characters and let the police deal with it. What is the probability that you guess correctly?

Answer 1

Soluion Given 米 ac possible alkbets in uppel Cose * 0-9 ie lo digits * SPeCia ChanaclenS , 5 Possib le Honts axe of its Ca CenSe ABCD 68" s eisible Q- The di femtt lange porks ake Posale on a Com on a Ca> belarjin? to ths Compony → ACCOMding to the above Conditon ะ:) Finst 4 LetenS Con be chosen with 9lepeafoton Mays (as)V Mays, then in() ะ> A special chevoeten in (to), mant keys Tn total (ac )4 )( lo)" many Possible license Plales

aphabets Specia drgts b The diffene license Plafese Possible fon a Can Compony if none of the ays To spot the lettens Then 5 mny kloys to phce a Special Then 02ny ays to place uo in belween So a many icense Plaes

C. The license Plates ane po9Sble fon a Con in this ComDantj i No alphabet on dt Can be heefed, 6 We choose 4 alphabets out 26 monyin among them Selve s imulalion3 Next (*) ผ0ys to close a speci D Ways To Place T total Plates al ways ทงก.ber Can be made

have emledl a Cai, but duxing Vocaien it is stolen To file a hepeit_T need t know the mumbo On the license Pla Can lemebe up to FRIG the ast deal With it Allokling siepe titon thee ane ossibl choices lon the last 3 digits and not allouing 3iepetition then ) (a)a/ manų Poss ble choices What T have chosen must be any One o them So pobability that T have guessed it,ightis alloling ne peiin) 5 to