1. A bag contains three red marbles, four green ones, one lavender one, two yellows, and five orange marbles.
How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?

2.If a die is rolled 35 times, there are 6^35 different sequences possible. The following question asks how many of these sequences satisfies certain conditions.
What fraction of these sequences have exactly 8 numbers less than or equal to 2? (Round your answer to four decimal places.)

3.Susan has seen a bag containing four red marbles, five green ones, two white ones, and two purple ones. She grabs eight of them. Find the probability in fractions that she has all of the red ones?

4.She has seen a bag containing three red marbles, two green ones, three white ones, and two purple ones. She grabs seven of them. Find the probability in fractions that she has at least one green one.

5. Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, two green ones, five white ones, and one purple one. She grabs five of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]
She has two red ones and one of each of the other colors.

6.Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, two green ones, four white ones, and three purple ones. She grabs five of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]
She has two green ones and one of each of the other colors.

7. Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]
She does not have all the red ones.

8. Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, three green ones, four white ones, and two purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]
She does not have all the green ones.

how much you paying?

1)792 sets with the lavender one and no yellow
1584 sets with one yellow exactly and no lavender.
total 2376.

2) p = 1/3 is the probability to get a number inferior or equal to 2 when rolling a dice.
when you roll a dice, either it's > 2 or <= 2.
X = number of rolls <= 2
p(X = 8) = 8*p^8*(1-p)^27 (Bernoulli)

3) 13 marbles total, 1287 possibilities in picking 8 marbles.
picking all reds mean that you pick 4 marbles (red), and 4 among the 9 remaining, ie 126 possibilities
p = 126/1287

4) 10 marbles total, 120 possibilities in picking 7 marbles
A is the event she picks at least 1 green
Ac the complementary event (she didn't pick any green one)
8 marbles those aren't green in total, so 8 possibilities in picking 7 marbles with no greens : p (Ac) = 8/120 = 1/15
p(A) = 1-p(Ac) = 14/15

I'll got quickly on 5-8 as they are similar

5) 12 marbles, 792 possibilities in picking 5 marbles
picking exactly 2 reds among 4 : 6 possibilities
picking 1 green among 2 : 2 possibilities
picking 1 white among 5 : 5 possibilities
picking 1 purple among 1 : 1 possibility

60 possibilities total : p = 60/792 = 5/66

6) 13 marbles total, 1287 possibilities in picking 5 marbles
2 green among 2 : 1 poss.
1 red among 4 : 4 poss.
1 white among 4 : 4 poss.
1 purple among 3 : 3 poss.

48 possibilities total : p = 48/1287 = 16/429

7) 10 marbles total, 45 possibilities total for 8 marbles
A denotes the event She does not have all the red ones.
Ac denotes the complementary event
p(Ac) = 15/45 = 1/3 thus p(A) = 2/3

8) 12 marbles total, 495 possibilities total for 8
A denotes the event She does not have all the green ones.
Ac denotes the complementary event
p(Ac) = 14/55 thus p(A) = 41/55

not sure how this is calculus (ie i dont see any epsilons and deltas) but anyway,

the key to probability is finding the total number of cases (the easy part) and then finding how many times a certain event occurs

for example, the first one,
total of 15 marbles
1. find the total number of ways you can get 5 marbles
2. find the total number of ways you can get exactly 1 lavender marble
3. find the total number of ways you can get exactly 1 yellow
4. subtract the overlap

what have you tried so far? usually on sites such as math.stackexchange, people show what work they've done so far using LaTeX...

Looks like she/he just waited for someone to give all the answers.