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Two team leaders- a girl and a boy has to be selected in a school. There are six boys and eight girls. Natasha does not become the team leader if Prakash also becomes the leader. Kapil will become the team leader only if Shilpa is the other team leader. Find the total number of ways in which the team leaders can be selected. 

Two team leaders- a girl and a boy has to be selected in a school. There are six boys and eight girls. Natasha does not become the team leader if Prakash also becomes the leader. Kapil will become the team leader only if Shilpa is the other team leader. Find the total number of ways in which the team leaders can be selected.  Correct Answer None of the above

Given:

Two team leaders- a girl and a boy has to be selected from six boys and eight girls

Natasha does not become the team leader if Prakash also becomes the leader

Kapil will become the team leader only if Shilpa is the other team leader

Concept:

To find the total number of ways, first the various cases possible pertinent to the situation has to be finalised. Then, number of ways of arranging in each of the cases possible has to be found out.

Calculation:

Natasha and Prakash cannot be selected together

Case 1: Natasha is selected. In this case, shilpa is not selected so, Kapil will also not be selected. One boy out of the remaining 4 can be selected in four ways

Case 2: Prakash is selected. Natasha will not be selected. One girl out of the remaining seven girls can be selected in 7 ways

Case 3: None of Natasha and Prakash is selected

Case 3 a: Kapil and Shilpa are selected = 1 way

Case 3 b: Shilpa is selected, Kapil is not selected = 4 ways (Kapil and Prakash are not selected)

Case 3 c: Shilpa and Kapil are not selected. Four boys and six girls remain. Number of ways = 4 × 6 = 24

Case 3 = 1 + 4 + 24 = 29

∴ Total number of ways = 4 + 7 + 29 = 40 

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