# Redundancy probability in employment

#### casy

##### New Member
The idea of being made redundant after working so many years in a company is everyone's nightmare.

I am currently working in a company employing 145 people (excluding management) where the management recently announced that 45 people out of the 145 will be made redundant in the very near future due to a fall in turnover of the Company and hence they need to cut down on Labour Force. However, they did not yet announce which people they are going to terminate his/her employment.Therefore, none of us (the145 people) currently know whose employment is going to be terminated.

In our Company there are 5 Divisions and in each division there are a number of people working in a number of Departments. (Say for example; Dept.1 = Accounting, Dept. 2= Sales&Marketing, Dept.3 = Design, Dept. 4= Production, Dept. 5= Human Resources.

The structure of the 5 Divisions are the same. That is to say, each Division has a Dept.1, Dept.2,Dept.3,Dept.4 and Dept. 5 in it but employing different amount of people in each department.

The Table below shows the configuration of our Company:

DIVISION DEPT.1 DEPT.2 DEPT.3 DEPT.4 DEPT.5 TOTAL
1 5 6 8 3 5 27
2 7 5 4 9 6 31
3 5 8 6 5 5 29
4 8 4 6 5 7 30
5 4 5 7 3 9 28
TOTAL 29 28 31 25 32 145

I am currently working in Division 5, Department 4.

In a real world, we would expect the management to take into consideration factors like experience, seniority, loyalty to the company, hard working etc. before deciding the termination of employment of each people.

But for the sake of the exercise, assume that all of the 145 people are equal. (i.e all 145 of us are experienced, hard working, etc.). The management therefore cannot make a distinction based on such factors. Hence the management (inorder to be fair to everyone) announced the following criteria for their forthcoming choices for termination of employment:

There shall be at least 2 persons from each Division,chosen randomly,
There shall be at least 1 person from each Department.chosen randomly.
As a person new to the concept of Probability, I want to calculate my chances of being made redundant under the above conditions.

Can anybody show me a step by step calculation.

#### hlsmith

##### Omega Contributor
Hmm. I see that a basic version can probably be calculated for part of this. But it looks plaguing when you have "at least" for division and department - I would imagine near countless outcomes when applying these.

Sorry for your bad news. If no one has addressed this by next Monday, I will take a try.

#### BGM

##### TS Contributor
The problem itself I guess is related to multihypergeometric distribution, but the calculation process is quite tedious.