Answer
$105$
Work Step by Step
If the set of five marbles includes exactly one yellow and no lavender, 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 lavender) out of 7. That is $C(7,4)=35$ This gives a total of $2*35=70$ different sets that include exactly one yellow marble and no lavender.
If the set of five marbles includes one lavender and no yellow ones, we can choose the other four marbles (not yellow and not lavender) out of 7. That is $C(7,4)=35$
The addition principle now tells us that the total number of sets of five marbles that include either the lavender one or exactly one yellow one but not both colors is $70+35=105$
