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The number of positive integers <1,00,000  which contain exactly one 2 , one 5 and one 7 in its decimal representation is

Option: 1

 2940


Option: 2

7350


Option: 3

2157


Option: 4

1582


Answers (1)

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Solution We may consider a 5-digit number as a number of the form
X X X X X

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 in 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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Ajit Kumar Dubey

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