ong>Given : A group of 5 employees needs to be selected for advanced training by the organization. These employees have to be selected out of FIVE managers: M1, M2, M3, M4, M5 and three interns: I1, I2, I3

The team should CONSIST of at least 3 managers and at least one Intern.

If M1 is selected, then M3 should not be selected

If M4 Is selected, then I2 should not be selected

To Find : All possible WAYS of selection

Solution:

Total to be selected = 5

4 - manager 1 intern

3 manager  2 intern

Case 1 :

4 Managers - 1 intern

M1 is selected, then M3 should not be selected

M1, M2, M4, M5  or  M2, M3, M4, M5

in both cases M4 is selected hence I2 can not be selected

so

M1, M2, M4, M5, I1

M1, M2, M4, M5, I3

M2, M3, M4, M5 , I1

M2, M3, M4, M5 , I3

Case 2 :  3 manager  2 intern

M1  M2 M4   I1 I3

M1  M2 M5   I1 I2

M1  M2 M5   I1 I3

M1  M2 M5   I2 I3

M1  M4 M5   I1 I3

M2 M3 M4   I1 I3

M2  M3 M5   I1 I2

M2  M3 M5   I1 I3

M2  M3 M5   I2 I3

M2 M4 M5   I1 I3

M3  M4 M5   I1 I3

Total ways of selection = 15

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