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:

Step-by-step solution

We know that any number is divisible by 9 if sum of the digits of the number is divisible by 9 . Now sum of the digits from 0 to 9 aligned &=0+1+2+3+4+5+6+7+8+9 &=45 aligned Hence to form 8 digits numbers which are divisible by 9 , a pair of digits either 0 and 9,1 and 8,2 and 7,3 and 6 or 4 and 5 are not used. Hence total number of 8 digits numbers which are divisible by 9 aligned &=8 (7 !)+7 (7 !)+7 (7 !)+7 (7 !) &+7 (7 !) &=36 (7 !) aligned