Question 1196575
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Give 5 of the 12 to the Frankos, then 4 of the remaining 7 to the Manchurs, then the remaining 3 to the Smiths:<br>
{{{C(12,5)*C(7,4)*C(3,3)=792*35*1=27720}}}<br>
OR...<br>
Give 3 of the 12 to the Smiths, then 5 of the remaining 9 to the Frankos, then the remaining 4 to the Manchurs:<br>
{{{C(12,3)*C(9,5)*C(4,4)=220*126*1=27720}}}<br>
or any of a few other different orders; the total number of ways of distrubuting the eggs does not depend on the order.<br>