A probability problem by A Former Brilliant Member

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?

The answer is 47.

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1 solution

For a quarrels to be happened, two persons are required and selecting them can be done in 12C2=12!/10!*2! ways=66ways. But this also include the quarrels between erstwhile(i.e former) Therefore, Total no. of ways=66-(4C2+3C2+5C2) =47.

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