Colombian license plates are made of 6 places. The rest 3 are letters, and the last 3 are numbers (e.g., XYZ123). a) How many license plates are possible taking into account that Colombian plates use the Spanish alphabet (and it has one more letter than the English alphabet, ñ)? b) How many different license plates can be formed if numbers and letters can not be used more than once?
Colombian license plates are made of 6 places. The rest 3 are letters, and the last 3 are numbers (e.g., XYZ123). a) How many license plates are possible taking into account that Colombian plates use the Spanish alphabet (and it has one more letter than the English alphabet, ñ)? b) How many different license plates can be formed if numbers and letters can not be used more than once?
a) To calculate the number of possible license plates when you can repeat letters and numbers, you can treat each character position as an independent choice.
There are 27 options for the 1st letter (26 letters of the English alphabet plus the letter "ñ" from the Spanish alphabet), 27 options for the 2nd, 27 options for the 3rd letter, 10 options for the 1st number, 10 options for the 2nd number, and 10 options for the 3rd number.
Hence, total possible choices = 27*27*27*10*10*10 = 19683000
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