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Question
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?
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Solution
Case I: 2-digit numbers more than 13, less than 20, formed from the digits 0, 1, 2, 5, 7, 8
Number of such numbers = 3
Case II: 2-digit numbers more than 20 formed from 0, 1, 2, 5, 7, 8
Using multiplication principle, the number of such numbers (repetition allowed)
= 4 × 6
= 24
Case III: 3-digit numbers formed from 0, 1, 2, 5, 7, 8
Using multiplication principle, the number of such numbers (repetition allowed)
= 5 × 6 × 6
= 180
All cases are mutually exclusive.
Required number = 3 + 24 + 180 = 207
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