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Subjects
Class 11MathematicsPermutations and CombinationsFundamental principle of countingHard
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A CAPTCHA has the form digit-letter-digit-letter-digit. Letters are chosen from (21) consonants with repetition, digits are distinct, and the middle digit is greater than the last digit. How many CAPTCHAs are possible?

Answer and explanation

Correct answer: (158760)

For the middle and last digits there are (45) ordered choices and the first digit has (8) choices; letters give (21^2) choices. Counting the inequality-based positions first is easier.

Related tags

Permutations-And-CombinationsFundamental-PrincipleCountingHardFundamental Principle Of CountingPermutations And CombinationsMathematicsClass 11 Mcq
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