Answer
$126$
Work Step by Step
If the set of five marbles includes exactly two red ones, we can choose these 2 reds out of 3 $C(3,2)=3$ different ways. We can choose the other three marbles (not red) out of 7. That is $C(7,3)=35$ This gives a total of $3*35=105$ different sets.
If the set of five marbles includes exactly three red ones (all of the red ones), we can choose the other two marbles (not red) out of 7. That is $C(7,2)=21$
So the total number of sets that include at least two red ones is $105+21=126$
