Q.

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

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a

∑n=49  nP4−n−1P3

b

∑n=49 P4   n

c

∑n=49 n−1P3

d

None of these

answer is A.

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Detailed Solution

The smallest number, which can occur in the middle is 4. The number of numbers with 4 in the middle=4P4−3P3.(∴ The other four places are to be filled by 0, 1, 2 and 3, and a number can not begin with 0)Similarly, the number of numbers with 5 in the middle =  5P4−4P3, etc.∴ The required number of numbers= 4P4−3P3+ 5P4−4P3+ 6P4−5P3+…+ 9P4−8P3=∑n=49  nP4−n−1P3
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