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

Shubham , 8 Years ago
Grade 12th pass
anser 1 Answers
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Last Activity: 8 Years ago

case 1 :- number does not contain 0.
from 1, 2, 3, 4, 5, 6, 7, 8, 9
choose 5 digits by
 \binom{9}{5} ways.
one number is largest which occupies middle place. arrange rest four numbers in 4! ways. thus
\binom{9}{5} X 4! =3024.
case 2 :- contains 0
choose other four numbers from 1,2,3,4,5,6,7,8,9 in 
\binom{9}{4 } ways. largest occupies third position.
no of ways numbers can be arranged = 3 X 3 X 2 X 1 =18
ways = \binom{9}{4 } X 18 = 2268
therefore our answer is 3024 + 2268 = 5292 

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