Every street in Canada is assigned a postal code. A postal code is made up of 3 letters and 3 digits that alternate. How many different postal codes can be created given the following conditions?

a) There are no restrictions.
b) The first letter must be S.
c) The first letter must be S and the first digit must be 7.

a) So if you are using 26 letters and 10 digits (0-9) would it be $26 \times 10 = 260$?

OR would it be $26 \times 26 \times 26 = 17576, 10 \times 10 \times 10 = 1000$, so with no restrictions, there would be 18576 different postal codes?

b) and c) I don't understand how to do these.


I assume that the description of postal codes is that they have to go like this: $$\tt(\text{letter})(\text{number})(\text{letter})(\text{number})(\text{letter})(\text{number})$$

Consider that a postal code is just a choice of first letter, first number, second letter, second number, third letter, and third number.

So, the number of postal codes (with no restrictions) is the number of ways of choosing the first letter, multiplied by the number of ways of choosing the first number, multiplied by (etc.)

Thus, your answer for part a) is incorrect. The correct answer is (mouse over to reveal)

$$26\times 10\times 26\times 10\times 26\times 10= 17,576,000$$

For b) and c), your choices are restricted. For example, if there is a specific letter position that you have to have an $S$ in, then the number of choices for that spot are 1, not 26.


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