Question

An eight digit number divisible by 9 is to be formed by using 8 digits out of the digits 0,1,2,3,4,5,6,7,8,9 without replacement.
The number of ways in which can be done is

• A. 2(7!)
• B. 4(7!)
• C. (36)(7!).
• D. (7!)(33)

Answer 1

The correct option is C

(36)(7!).

From the digits 0 1 2 3 4 5 6 7 8 9

The sum is 45

Thus, every time we remove 2 digits which add up to 9, we will have a new set of 8 numbers which are divisible by 9

Case 1

Removing 0 and 9

Number of cases possible = 8!

Case 2

Removing

(1)8 and 1

(2)7 and 2

(3)6 and 3

(4)5 and 4

In each case, total number of cases = 8!-7!

(we subtract 7! Because those are the cases where 0 is the first digit)

Hence, total number of ways = 4(8!-7!)+8!= 36x7!.