Question

7. Suppose that in a certain state, all automobile license plates have three uppercase letters followed by three digits. (a) (5 points) How many different license plates are possible? (b) (5 points) How many license plates could begin with A, end in 0, and in which all the letters and digits are distinct? (c) (5 points) What is the probability that a randomly chosen license plates begins with A, ends with O, and all its letters and digits are distinct?

Answer 1

solution W3 digits. (a) Number of possible license plates, license places have three upper case letters followed = 26x26 8 26x lo xlox lo At each position each of place digits placed At each these any of the 26 letters position any of the cay ed lo Hence, Number 3 possible license plates - 17576000 (6 Number with the letters & license plates beginning, are diſtinct. = 1 x 25 x 24 x 9 x B x 1 A At first position we At sixth position we can place only can place only a B612

more periton can be filled by remaboy sa presition con be filled by remering filled by remaining filled by remaining digles 4th position con be 9 digits can be Number of such license plates 43200 (c) Probability, f of fourunable Number outcomes Number possible outcomes total No 43200 17576000 P = 0.0024 This is the probability that a Shandomly ends with O. & all its letters & distinct. digits are B612 1 2