Answer
50
Work Step by Step
If the set of five marbles includes exactly one yellow, we can choose this yellow marble out of 2 $C(2,1)=2$ different ways. We can choose the other four marbles (not yellow and not green) out of 6. That is $C(6,4)=15$ This gives a total of $2*15=30$ different sets that include exactly one yellow marble, but no green ones.
If the set of five marbles includes two yellow ones we can choose the other three marbles (not yellow and not green) out of 6. That is $C(6,3)=20$
The addition principle now tells us that the total number of sets of five marbles that include at least one yellow one but no green ones is $30+20=50$
