Find the number of integers greater than 7000


Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated. [Hint: Besides 4-digit integers greater than 7000, five digit integers are always greater than 7000.]


According to the question,

Digits that can be used = 3,5,7,8,9

Since, no digits can be repeated,

The number of integers is 5P5 = 5! = 120

For a four-digit integer to be greater than 7000,

The four-digit integer should begin with 7,8 or 9.

The number of such integer = 3 × 4P=3 × 4P= 3(24) =72

Therefore, the total no of ways = 120+72 = 192

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