Question

In a certain state, license plates consist of three letters followed by three numbers. 1. How many different license plates can be made if the letter and number carn repeat? (5pts) appears more than once? (5pts) number appears more than once? (5pts) 2. How many different license plates can be made in which no letter or number 3. A license plate is chosen at random. What is the probability that no letter or

Answer 1

Letters range from A to Z: total range 26

Numbers range from 0 to 9: total range = 10

1) Number of different license plates can be made if the letter and number can repeat

= 10*10*10*26*26*26

( as each letter can be selected in 26 ways and a number can be selected in 10 ways)

2) Number of different license plates can be made if the letter and number can not repeat

= 10*9*8*26*25*24

( as each letter can be selected in 26 ways and not repeated then leftover letters are 25 and for 3rd time we have 24 choices and. Same logic for numbers)

3)

P(no letter or number appears more than once)

= 1 / Number of different license plates can be made if the letter and number can not repeat

= 1/(10*9*8*26*25*24)