Q. An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :

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Solution:

Eight digit no divisible by 9 i.e. sum of digits divisible by 9
(i) Total no formed by 1,2,3,4,5, 6,7,8 = 81
(ii) Total no formed by 0,2,3,4,5,6,7,9 = 77!
(iii) Total no formed by 1,0,3,4,5,6,9,8 = 77!
(iv) Total no formed by 1,2,0,4,5,9,7,8 = 77!
(v) Total no formed by 1,2,3,0,5,6,7,8 = 77!
8! + 28 7 !
= 36 7 !