self Maths Puzzle

Three business entities X Ltd, Y Ltd. and Z Ltd, with 4, 3 and 5 employees respectively, merged into XYZ Ltd in order to jointly raise the capital for setting up a new modern production plant in Jaipur. After two years, on the question of management decisions on the new venture at Jaipur, the employees started adopting differing viewpoints and began to quarrel among themselves. Given the fact that there is no quarrel among the employees of the erstwhile (i.e. former) X Ltd, Y Ltd and Z Ltd, what could be the maximum number of quarrels that can take place within XYZ Ltd?

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self Other Question

In a cricket match, Team A scored 232 runs without losing a wicket. The score consisted of byes, wides and runs scored by two opening batsmen: Ram and Shyam. The runs scored by the two batsmen are 26 times wides. There are 8 more byes than wides. If the ratio of the runs scored by Ram and Shyam is 6:7, then the runs scored by Ram is
PQRSTU is a regular hexagon drawn on the ground. Prashant stands at P and he starts jumping from vertex to vertex beginning from P. From any vertex of the hexagon except S, which is opposite to A, he may jump to any adjacent vertices. When he reaches S, he stops. Let Sn be the number of distinct paths of exactly n jumps ending at S. What is the value of S2k, where k is an integer?