Permutations
Question
The number of positive integers < 1,00,000 which contain exactly one 2, one 5 and one 7 in its decimal representation is
Moderate
Solution
where X 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 any of the 3-remaining places.
The remaining 2 places can be filled up by 7 digits.
Thus, there are (5) (4) (3) (7) (7) = 2940 positive integers in the desired category
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