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Question

The number of natural numbers less than $$1000$$ in which no two digits are repeated is:


A
738
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B
792
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C
837
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D
720
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Solution

The correct option is C $$738$$
Numbers less than $$1000$$ are one digit no., two digits numbers and three digits number.
No. of one digit number $$= 9$$
No. of two digit number in which $$= 9\times 9 = 81$$
no. two are repeated
(For one's place we have 9 choice for ten's place we have 9 choices (0 excluded) )
No. of three digit number in which  No. two digit are repeated $$=9\times 9 \times 8$$
                                                                                                         $$=648$$
(For hundred place we have 9 choice  (0 excluded)  for ten's place we have 9 choices & or One's place we have 8 choices  )
$$\therefore$$ Total number less than 1000 in which no. two digits are repeated are : $$ =9+81+648$$
                                                                                                                           $$= 738$$

Mathematics

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