1: In Pottsylvania, the license plates on cars are made up of 7 characters. capital letters may be used as well as the digits from 0-9. The first three must be digits, the next two must be letters, the sixth character must be a digit, and the final character be may be either a letter or a digit.

If letters may be repeated but digits may not, how many license plates are possible?

2: A couple is planning on having 3 children. Using B for boy and G for girl, calculate the following:

a) The sample space of all possible birth orders. (Notes: Order matters. list them out

b) The probability that all three children are of the same sex.

c) The probability that an even number of boys is born.

3: A survey was taken amongst people about their food preferences the results were:

37 like pizza
33 like ice cream
34 like eclairs
20 like pizza and eclairs
18 like pizza and ice cream
14 like ice cream and eclairs
15 preferred different food choices

a) Draw and fill out a Venn diagram that represents this problem?

b) Based on your Venn diagram, how many people liked exactly 1 of the offered choices?

c) if a person were picked at random, what is the probability that they like at least 2 of the choices offered?