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Q.

How many numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition of digits is allowed) ?

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a

1024

b

810

c

2346

d

None of these

answer is B.

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Detailed Solution

Case I : When number in two digits.Total number of ways  =9C1×9C1=9×9=81Case II : When number in three digits Total number of ways =9C1×9C1×9C1=9×9×9=729∴ Total number of ways = 81+ 729 =810
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How many numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition of digits is allowed) ?