Let the engineer visits the factory first time after x1​ days to 1 June, second time after x2​ days to first visit and so on.x1​+x2​+x3​+x4​+x5​=11∴x1​+x2​+x3​+x4​+x5​=11where x1​,x5​≥0 and x2​,x3​,x4​≥1 according to the requirement of the question.Now, let x2​=a+1,x2​=b+1 and x4​=c+1 where a,b,c≥0∴ New equation will bex1​+a+b+c+x5​=8Now, the number of all possible ways in which the engineer can made visits is equals to the non-negative integral solution of equationx1​+a+b+c+x3​=8, and it is equal to8+5−1C5−1​=12C4​=4×3×212×11×10×9​=495.