A seven digit number divisible by 3 is to be formed using 7 out of numbers 1, 2, 3, , 9. The number of ways in which this can be done is

Sum of the seven digits use must be a multiple of 3. As 1 + 2 + + 9 = 72,

we mustuse one of the following pairs: (1, 2), (1, 5), (1, 8), (2, 4), (2, 7), (3, 6), (3, 9), (4, 5), (4, 8), (5, 7), (6, 9), (7, 8)

Thus, required number of ways is (12) (7!)