The number of positive integers which contain exactly one 2 , one 5 and one 7 in its decimal representation is
2940
7350
2157
1582
Solution We may consider a 5-digit number as a number of the form
where is a digit from 0 to 9 . The digit 2 can occupy any of the five places, 3 can occupy any of the remaining 4 places and 7 in any of the 3-remaining places. The remaining 2 places can be filled up by 7 digits. Thus, there are
positive integers in the desired category.
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