Question:
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.]
Solution:
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 × 4P3 =3 × 4P3 = 3(24) =72
Therefore, the total no of ways = 120+72 = 192
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