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1.) In the coming state elections, Bharat Mata Party
(BMP) will contest for 77 assembly seats. As BMP's majority
vote bank is distributed amongst three communities viz. A,
B and C, it will give election tickets only to those
workers who belong to these communities. The workers of
communities B and C are split into factions. Every faction
of community B has 15 workers and that of community C has
25 workers. There were no factions among the workers
belonging to community A. If BMP gives a ticket to a
worker, it must give tickets to every other worker
belonging to the same faction. BMP distinguishes between
any two workers only on the basis of their communities. In
how many ways can BMP distribute its election tickets
giving at least one ticket to each community?
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