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Question
A code word consists of three letters of the English alphabet followed by two digits of the decimal system. If neither letter nor digit is repeated in any code word, then the total number of code words is:
A code word consists of three letters of the English alphabet followed by two digits of the decimal system. If neither letter nor digit is repeated in any code word, then the total number of code words is:
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Solution
The correct option is A 1404000
The first letter of the code can be chosen from the 26 letters in 26 ways. Since no letter is repeated the second letter can chosen in 25 ways and the third letter can be chosen in 24 ways. Similarly there are 10 ways for the first digit and 9 ways for the second digit.
Hence the total number of ways to generate the code is 26×25×24×10×9=14,04,000
The first letter of the code can be chosen from the 26 letters in 26 ways. Since no letter is repeated the second letter can chosen in 25 ways and the third letter can be chosen in 24 ways. Similarly there are 10 ways for the first digit and 9 ways for the second digit.
Hence the total number of ways to generate the code is 26×25×24×10×9=14,04,000
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