An electronics retailer wants to send codes for $10 off a pair of headphones to the subscribers of its e-mail list. The coupon code will have two letters followed by three digits. The letters A, B, C, and D and the digits 6 and 9 will not be used. So, there are 22 letters and 8 digits that will be used. Assume that the letters and digits can be repeated. How many such coupon codes can be generated?couponcodes
Question
An electronics retailer wants to send codes for $10 off a pair of headphones to the subscribers of its e-mail list. The coupon code will have two letters followed by three digits. The letters A, B, C, and D and the digits 6 and 9 will not be used. So, there are 22 letters and 8 digits that will be used. Assume that the letters and digits can be repeated. How many such coupon codes can be generated?couponcodes
Solution
The number of possible coupon codes can be calculated by multiplying the number of possibilities for each character in the code.
For the first two characters, there are 22 possible letters. Since letters can be repeated, there are also 22 possibilities for the second character.
For the last three characters, there are 8 possible digits. Since digits can be repeated, there are also 8 possibilities for each of the last three characters.
So, the total number of possible coupon codes is 22 * 22 * 8 * 8 * 8 = 2,985,984.
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