question 1

A student is planning a spring break vacation. The vacation packages that she is considering purchasing have a variety of options. She can go to Mexico or Florida, stay in an all -inclusive resort, a bed and breakfast, or a condo, and choose a room with either an ocean view or a court-yard view.

1) How many different vacation packages are there?

(Record your answer to the nearest whole number in the first blank below)

2) How many different vacation packages are there if the student MUST stay in a condo?

(Record your answer to the nearest whole number in the second blank below)

Question 2

In Canada, all postal codes are made up of six characters, which follow the pattern:letter-digit-letter-digit-letter-digit.

The first letter of the code identifies a specific region. Each of the remaining two letters in the postal code can be any of 20 letters, and each of the three digits can be any digit from 0 to 9. All letters and digits can be repeated. In Alberta, all postal codes start with the letter T.

How many different postal codes are possible in Alberta?

(Record your answer to the nearest whole number in the blank below)

question 3

In 1912, Alberta licence plates consisted of four digits. Each digit could be repeated, but the first digit could not be zero. By 1990, Alberta licence plates consisted of six digits. Each digit could be repeated, but the first digit could not be zero.

Compared with the number of licence plates available in 1912, find the increase in the number of licence plates available in 1990.

question 4

Recall the example about Louie's Bistro.You had a choice of 2 salads, mixed or Caesar.You had a choice of 4 entres: chili, club sandwich, roasted chicken, or grilled fish. Finally , for dessert, you could choose a brownie, a cupcake, or a piece ofcheesecake.

How many different meals are possible if you do not have to choose an item from each category?

(Record your answer to the nearest whole number in the blank below)

Question 5

Karen has a bank card that requires a 4-digit PIN number. All digits from 0 to 9 can be used.

a) How many PINs are possible if digits can repeat?

(Record your answer to the nearest whole number in the first blank)

b) How many PINs are possible if digits cannot repeat?

(Record your answer to the nearest whole number in the second blank)

c) How many PINs are possible if the first digit must be a 7 and digits cannot repeat?

(Record your answer to the nearest whole number in the third blank)

Question 6

A group of 8 teenagers are lined up to buy tickets to a rock concert. How many possible arrangements of teenagers are there?

Leave your answer in factorial notation.