Section 3.2

2) Airports are identified with 3-letter codes. For example, Richmond, Virginia has the code RIC, and Memphis, Tennessee has MEM. How many different 3-letter codes are possible?

1. choose first letter (26)

2. choose second letter (26)

3. choose third letter (26)

   $26^3$

4) In ordering coffee you have a choice of regular or decaf; small, medium or large; here or to go. How many different ways are there to order a coffee?

1. choose reg or decaf. (2)

2. chose lg, med, sm. (3)

3. choose here or togo (2)

   2 x 3 x 2 = 12

6) You toss a coin, then roll a dice, and then draw a card from a 52-card deck. How many different outcomes are there? How many outcomes are there in which the dice lands on 3? How many outcomes are there in which the dice lands on an odd number? How many outcomes are there in which the dice lands on an odd number and the card is a King?

1. specify coin result (2)

2. specify die result (6)

3. specify card chosen (52)

   2 x 6 x 52

1. specify coin result (2)

2. specify die is 3 (1)

3. specify card chosen (52)

2 x 1 x 52

1. specify coin result (2)

2. specify die as 1,3, or 5 (3)

3. specify card chosen (52)

   2 x 3 x 52

1. specify coin result (2)

2. specify die as 1,3, or 5 (3)

3. specify card as king (4)

2 x 3 x 4

8) A coin is tossed 10 times in a row. How many possible sequences of heads and tails are there?

(x,x,x,x,x,x,x,x,x,x)

1. Specify flip 1 (2)
2. Specify flip 2 (2)
3. Specify flip 3 (2)
4. Specify flip 4 (2)
5. Specify flip 5 (2)
6. Specify flip 6 (2)
7. Specify flip 7 (2)
8. Specify flip 8 (2)
9. Specify flip 9 (2)
10. Specify flip 10 (2)

$2^{10}$

10) A dice is tossed four times in a row. There are many possible outcomes, such as (2,6,6,3), or (3,3,3,3). How many different outcomes are possible?

1. Specify roll 1 (6)
2. Specify roll 2 (6)
3. Specify roll 3 (6)
4. Specify roll 4 (6)

$6^4$