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Permutations and Combination — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsPermutations and Combination2 Marks
Question
How many four-digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?
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Answer

Between any set of digits, the greatest number is possible when digits are arranged in descending order. ∴ 7432 is the greatest number, formed from the digits 2, 3, 4, 7. Since a 4-digit number is to be formed from the digits 2, 3, 4, 7, where repetition of the digit is not allowed, 1000’s place digit can be selected in 4 ways, 100’s place digit can be selected in 3 ways, 10’s place digit can be selected in 2 ways, Unit’s place digit can be selected in 1 way. ∴ Total number of numbers not exceeding 7432 that can be formed with the digits 2, 3, 4, 7 = Total number of four-digit numbers possible from the digits 2, 3, 4, 7 = 4 × 3 × 2 × 1 = 24

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