The number of ways in which we can arrange the digits 1, 2, 3, …, 9 such that the product of five digits at any of the five consecutive positions is divisible by 7 is

Let an arrangement of 9 digit number be  x1x2x3x4x5x6x7x8x9.Note that we require product of each of x1,x2,x3,x4,x5;x2,x3,x4,x5,x6;…;x5,x6,x7,x8,x9 is divisible by 7.This is possible if the 5th digit is 7.Therefore, we can arrange the 9 digits in desired number of  ways in 8! ways.