Question 1121121
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Let the four flavors be represented by V, C, S, and P.  The number of different ways of distributing the cones among the four children is the number of different arrangements of the letters<br>
VVCCCSSSSP<br>
By a well-known counting principle, that number of different ways is<br>
{{{(10!)/((2!)(3!)(4!)(1!)) = 12600}}}