Answer
$126$
Work Step by Step
If the set of five marbles includes exactly one red, we can choose this red marble out of 3 $C(3,1)=3$ different ways. We can choose the other four marbles (not red) out of 7. That is $C(7,4)=35$ This gives a total of $3*35=105$ different sets that include exactly one red marble.
If the set of five marbles includes no red ones we can choose the other five marbles (not red) out of 7. That is $C(7,5)=21$
The addition principle now tells us that the total number of sets of five marbles that include at most one yellow one is $105+21=126$
