Answer
$196$
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) out of 8. That is $C(8,4)=70$ This gives a total of $2*70=140$ different sets that include exactly one yellow marble.
If the set of five marbles includes exactly two yellow ones (all of the yellow ones), we can choose the other three marbles (not yellow) out of 8. That is $C(8,3)=56$
So the total number of sets of five marbles that include at least one yellow one is $140+56=196$
