105717
number of 9 digits numbers divisible by 9 using the digits from 0 to 9 if each digit is used atmost once is K.8!, then k has value equal to?
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3 Answers
2305For a number to be divisible by 9,the sum of the digits should be divisible by 9.
Case 1:(if there is no 0 in the number )
Sum of digits = 45 (divisible by 9)
No. of possible arrangements of the digits = 9!.
Case 2:(if the no. has a 0)
0 must replace some digit.If it replaces any digit other than 9 then the sum does not remain divisible by 9.
Hence the number does not contain 9 in this case.
0 can be placed in any of the 8 positions (because 0 cannot be placed as the first digit)
The rest of the 8 digits can be placed in 8! ways.
\thereforeTotal no. of digits = 9!+8*8!=17*8!
k=17
Swarna Kamal Dhyawala thanxUpvote·0· Reply ·2013-03-20 10:35:22
