In Florida, license plates consist of a list of up to six symbols chosen from 26

Question

In Florida, license plates consist of a list of up to six symbols chosen from 26 letters of the alphabet and the ten digits, and can be either a "regular" plate, or a "state" plate (which is yellow). A license plate number that appears on a regular plate can also appear on a state plate. a. How many license plates are possible if repetition of symbols is allowed? b. How many license plates are possible if repetition of symbols is not allowed? c. What is the probability of randomly choosing a plate that has a repeated symbol? a. A small town has 800 residents. Must there be three people with the same birthday? Why or why not? b. In the same town, must there be two people with the same first and last initials? Why or why not? a. Suppose your sock drawer contains 5 pairs of white socks and 5 pairs of black socks. How many socks must you pick at random from the drawer to be sure you have a matched pair? b. How many integers from 1 to 100, inclusive, must you pick to be sure of getting one that is divisible by 5?

Explanation / Answer

Problem 3)a)

5 pair of socks and 5 pairs of balck = 20 socks

we have to pick 3 socks to have a matched pair

b) total integers not divisible by 5 from 1 to 100 are 80

we have to pick 81 integers to be sure of getting one

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