JEE Advanced Mathematics question

The total number of 5-digit numbers of different digits in which the digit in the middle is the largest is

Answer: (D)

Solution

Let the middle digit be . The other four digits must be distinct and smaller than , i.e. chosen from ( digits), so .

For a fixed : arrangements of 4 of these digits in the four outer places ; those with 0 in the leading place . So the count

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Question ID VK-108153