The number of all positive integers up to 500 with non-repeating digits is
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Explanatory Answer
Single digit numbers where none of the digits is repeated = 1 to 9
⇒ n(single digit numbers)= 9
Double digit numbers = AB (where A is any number from 1 to 9 and B is any number except A)
⇒ n(double digit numbers) = 9 × 9 = 81
Triple digit numbers = ABC (where A is any number from 1 to 4, B is anything except A and C is anything except A, B)
⇒ n(triple digit numbers) = 4 × 9 × 8 = 288
Total number of numbers = 288 + 81 + 9 = 378
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