Permutations #1
Probability
Level
3
Determine the number of natural numbers smaller than , in the decimal notation of which all digits are distinct.
The answer is 5274.
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1 solution
Total number of 4 digit natural numbers with distinct digits = P ( 1 0 , 4 ) − P ( 9 , 3 )
Total number of 3 digit natural numbers with distinct digits = P ( 1 0 , 3 ) − P ( 9 , 2 )
Total number of 2 digit natural numbers with distinct digits = P ( 1 0 , 2 ) − P ( 9 , 1 )
Total number of 1 digit natural numbers with distinct digits = 9
Hence total number of numbers = 5 2 7 4