Question
Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9, no digit being repeated.

192

111

543

None of these
easy
Solution
192
A five digit integer is always greater than 7000. The number of such integers is ^{5}P_{5} = 5! = 120. For a four digit integer to be greater than 7000, it must being with 7, 8 or 9. The number of such integers is 120 + 72. Hence, the required number of such integers is 120 + 72 = 192.
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