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Q.

By using the non-zero digits, the number of 5 digit numbers that can be formed so that each number has largest digit in its middle place and the digits in the number are different is

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a

r=49P4   r

b

r=48P4   r-r=48P3   r

c

r=48P3   r

d

r=48P4   r

answer is D.

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Detailed Solution

 

 

Middle digit=5   Remaining 4 places can be filled using 1, 2, 3, 4 is 4p4 ways  

middle digit=6Remaining 4 places can be filled in using 1, 2, 3, 4, 5 in 5p4  ways.

Middle digit=7using 1, 2, 3, 4, 5, 6 remaining 4 places can be filled in 6p4 ways.

Middle dight=8using 1, 2, 3, 4, 5, 6, 7 remaining 4 places cab be filled in 7p4 ways.

Middle digit=9using 1, 2, 3, 4, 5, 6, 7, 8 remaining 4 places can be filled in  8p4 ways.

 Total no. of 5digit numbers=r=48 rP4                                             

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