document.write( "Question 1030326: A hotel reservation number consists of 5 numbers followed by 3 letters. How many different reservation numbers are possible? \n" ); document.write( "

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\n" ); document.write( "Question:
\n" ); document.write( "A hotel reservation number consists of 5 numbers followed by 3 letters. How many different reservation numbers are possible?
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\n" ); document.write( "Solution:
\n" ); document.write( "From the context of the question, repetition of digits or letters are allowed.
\n" ); document.write( "For each digit, there are 10 possible choices (even a leading zero is considered a reservation number), and for each letter, there are 26 letters (normally upper and lower cases are considered identical).
\n" ); document.write( "Since this can be considered as an eight-step experiment, we can multiply the number of possible choices for each position to get
\n" ); document.write( "N=10*10*10*10*10*26*26*26
\n" ); document.write( "=10^5*26^3
\n" ); document.write( "=1757600000
\n" ); document.write( "Answer: there are 1757600000 possible reservation numbers.
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\n" ); document.write( "Note: usually at least one digit is reserved as a check digit to avoid communication errors such as wrong digit, letter or inversions.
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