The total number of 5 digit numbers of different digits in which the digit in the middle is the largest, is -
– 
Text Solution
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Since the largest digit is in the middle, the middle digit is greater than or equal to 4, the number of numbers with 4 in the middle = 4 P 4 – 3 P 3 .
( the other four places are to be filled by 0, 1, 2, and 3, and a number cannot begin with 0). Similarly, the number of numbers with 5 in the middle = 5 P 4 – 4 P 3 , etc.
∴ The required number of numbers
= ( 4 P 4 – 3 P 3 ) + ( 5 P 4 – 4 P 3 ) + ( 6 P 4 – 5 P 3 ) +…. + ( 9 P 4 – 8 P 3 )
= 
.
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