Question 1095210
<br>A straightforward application of the fundamental counting principle, plus the "n choose r" concept.  I will suppose that, since you are asking this kind of question, that you are familiar with both of those.<br>
You need to choose 3 of the 8 red marbles; by definition, that is the number "8 choose 3", which is
{{{(8*7*6)/(3*2*1) = 56}}}<br>
Similarly you need to choose 4 of the 5 blue marbles (5 choose 4, which is 5) and 2 of the 4 green marbles (4 choose 2, which is 6).<br>
Then the fundamental counting principle says that the number of ways of choosing 3 of the 8 red marbles AND 4 of the 5 blue marbles AND 2 of the 4 green marbles is
{{{56*5*6 = 1680}}}<br>
Yes, that is a 4-digit number with a digit sum of 15....