Question 1204021
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In solving a problem like this, it is useful to know that the different grades can be assigned in any order; the result will be the same.  For example, if the grades are assigned from lowest (F) to highest (A), then the calculation is<br>
{{{C(16,3)*C(13,2)*C(11,3)*C(8,6)*C(2,2)=(560)(78)(165)(28)(1)=201801600}}}<br>
Of course the last factor {{{C(2,2)}}} is not needed -- but showing it makes the complete process more clear.<br>
And a third way to find the answer to the question is to count the number of different ways of arranging the 16 grades in a string:<br>
AABBBBBBCCCDDFFF<br>
By a well-known counting principle, the number of distinct arrangements of those letters is<br>
{{{16!/((2!)(6!)(3!)(2!)(3!))=201801600}}}<br>