Here As mention "at least 1"
Given data : 11 new Employees, 4 subdivision. Condition: at least one employee should go each subdivisions.
Required No. of ways= Total ways without restriction - total ways which violates the restriction
Total ways without restriction:
(use 11 employees as set 1 and 4 subdivisions as set 2)
i.e. total possible mapping= 411
Total ways which violates the restriction:
=all employees mapped to any of 3 subdivisions+ all employees mapped to any of 2 subdivisions + all employees mapped to any of 1 subdivisions
= 311 * C(4,3) - 211 * C(4,2) + 111 * C(4,1) (here i have to use - for explanation watch the video link given in comment of Arjun's sir Answer.)
= 7,20,880
Required No. of Ways= 411 - 311 * C(4,3) + 211 * C(4,2) - 111 * C(4,1)
= 34,98,000