Q.
A seven-digit number without repetition and divisible by 9 is to be formed by using seven digits out of 1,2,3,4,5,6,7,8,9. The number of ways in which this can be done is
Sum of 7 digits is a multiple of 9 . Sum of numbers 1,2,3,4,5,6,7,8,9 is 45 ; so two left digits should also have sum of 9 . The pairs of left numbers are (1,8),(2,, 7), (3,6),(4,5). With each pair left number of 7 -digit number is 7! So with all 4 pairs, total number is 4×7!.