Question

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

A
738
B
792
C
837
D
720

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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