Question 1206426
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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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<pre>
The total number of different partitions of 30 into the union of 16 and 14 is

    {{{C[30]^16}}} = 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) = {{{C[30-2]^(16-2)}}} + {{{C[30-2]^(14-2)}}} = {{{C[28]^14}}} + {{{C[28]^12}}} = 40116600 + 30421755 = 70538355.


The probability is  {{{favorable/total}}} = {{{70538355/145422675}}} = {{{211/435}}} = 0.4851 (rounded).
</pre>

Solved.


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The formulas are self-explanatory.