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

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

Permutations and Combinations

Solution:

Number of one digit natural number $= 9$
Number of two digit natural numbers with different digits $= 9 \times 8$
Number of three digit natural number with different digits $= 9 \times 8 \times 7$
Total number of natural number $<\, 1000$ with number of digit is repeated $= 9 + 72 + 504$
$=585$.