Question 1204839
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The statement of the problem is not clear, leading to different possible interpretations.  My interpretation differs from that shown in the response from tutor @Edwin in two ways. (1) The problem does not say that each child must get at least one candy, so the numbers each child gets are non-negative integers, not positive integers. (2) The number of candies each of the twins gets is not important; the only requirement is that together they get 7 pieces.<br>
With that interpretation....<br>
Take the 7 pieces of candy and give them to the twins (to be shared between them in any way).<br>
That leaves 11 pieces of candy to be divided among the other three children.  Using the "stars and bars" process, there are 11 stars (the pieces of candy) and 2 bars (to divided the stars (candies) into 3 groups). The number of ways to distribute the candies is then the number of ways of arranging the symbols<br><pre>
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By a well-known counting principle, that number ways is<br>
{{{13!/((11!)(2!))=C(13,2)=78}}}<br>
ANSWER (with this interpretation): 78<br>