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GMATinsight
In how many no. between 100 and 1000 exactly Two of the digits is 5?

(A) 648
(B) 512
(C) 252
(D) 225
(E) 26

Source: https://www.GMATinsight.com

It's simple can be solved by elimination of answer choices.

Option A and B are too large, not possible. Even C & D are large to have correct choice.

Ans : E

Alternatively
X55 --- 8 possibility
5X5 --- 9 possibility
55X --- 9 possibility

8+9+9=26

Ans E
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Deconstructing the Question
We are counting 3-digit numbers (from 100 to 999) with exactly two digits equal to \(5\).
Key idea: choose which 2 positions are \(5\), then count choices for the remaining digit, respecting that the hundreds digit cannot be 0.

Step-by-step
There are \(\binom{3}{2}=3\) ways to place two 5s among the three positions.

Case: \(55U\)
\(U\ne 5\) gives \(9\) choices.

Case: \(5T5\)
\(T\ne 5\) gives \(9\) choices.

Case: \(H55\)
Hundreds digit \(H\) can be \(1\) to \(9\) but not \(5\), so \(8\) choices.

Total:
\(9+9+8=26\)

Answer: E
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