JEE Advanced 2025 Mathematics question
Let S be the set of all seven-digit numbers that can be formed using the digits 0, 1 and 2. For example, 2210222 is in S, but 0210222 is NOT in S. Then the number of elements x in S such that at least one of the digits 0 and 1 appears exactly twice in x, is equal to .
Answer: 762
Solution
Let A = "exactly two 0s" and B = "exactly two 1s"; the first digit cannot be 0. |A|: the two 0s go in positions 2–7, ways, and the other 5 places get 1 or 2: 15 × 32 = 480. |B|: all strings with exactly two 1s,
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