Bismarck wrote:

Of the three-digit integers greater than 750, how many have at least two digits that are equal to each other?

(A) 56

(B) 70

(C) 72

(D) 74

(E) 78

The total possibilities of numbers greater than 750 where all digits are different

From 750 to 799 - 1*4*8 = 32 (as 7 can't be part of the ten's or one's digit)

From 800 to 899 - 1*9*8 = 72 (the second digit can take any other values except 8)

From 900 to 999 - 1*9*8 = 72 (the second digit can take any other values except 9)

The 3-digit numbers greater than 750 with all digits different are 32+72+72 = 176

The 3-digit numbers greater than 750 with at least 2 digits that are equal are 250 - 176 or 74.

Therefore, the 3-digit numbers greater than 750 where at least 2 digits are equal to each other are

74(Option D)
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