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: 11, 12, 13) according to the given criteria: 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 12 should not be selected
Answers
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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