Question

a pizza chain wants to send codes for $2 off a large pizza to the subscribers of its e - mail list. each coupon code will have three letters followed by two digits. the letters m, n, and o and the digits 1, 3, 5, and 7 will not be used. so, there are 23 letters and 6 digits that will be used. assume that the letters and digits can be repeated. how many such coupon codes can be generated?

Explanation:

Step1: Calculate letter combinations

Since repetition is allowed, each of the 3 letter positions has 23 choices. The number of letter sequences is $23 \times 23 \times 23 = 23^3$.
$23^3 = 12167$

Step2: Calculate digit combinations

Each of the 2 digit positions has 6 choices. The number of digit sequences is $6 \times 6 = 6^2$.
$6^2 = 36$

Step3: Find total coupon codes

Multiply the number of letter and digit sequences to get the total number of unique coupon codes.
$12167 \times 36$

Answer:

438012 coupon codes