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Q) Determine the number of natural numbers smaller than 10^4, in the decimal notation of which all the digits are distinct.

Asked by Anish 29th November 2018, 11:38 AM
Answered by Expert
Answer:
According to the question, the number of natural numbers smaller than 104 in the decimal notation in which all the digits are distinct are
The required number consists of 4 digit, 3 digit, 2 digit and 1 digit.
Total number of 4 digit natural number = begin mathsize 16px style straight P presuperscript 10 subscript 4 minus straight P presuperscript 9 subscript 3 end style.........(i)
Total number of 3 digit natural number = Error converting from MathML to accessible text.........(ii)
Total number of 2 digit natural number = Error converting from MathML to accessible text.........(iii)
Total number of 1 digit natural number = Error converting from MathML to accessible text..........(iv)
The required number of natural numbers is sum of all (i), (ii), (iii) and (iv) we get 5274

Answered by Expert 29th November 2018, 6:27 PM
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