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A sports master divides randomly a class of 30 students into 2 football teams
of 16 and 14 students respectively. Find the probability that two particular students,
Muthu and Ali, will be in the same team.
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The total number of different partitions of 30 into the union of 16 and 14 is
= 145422675.
The number of favorable partitions is the sum "they both are in a 16-team" + "they both are in a 14-team"
#(16,2) + #(14,2) = + = + = 40116600 + 30421755 = 70538355.
The probability is = = = 0.4851 (rounded).
Solved.
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The formulas are self-explanatory.