Please answer this question -

1.. Fifteen patients must be assigned to one of three doctors. If each doctor must get at least 4 patients then how many different ways can the patients be assigned?

2.. Six friends go to their favorite restaurant, which has ten different dinners on the menu. If the friends are equally likely to pick any of the dinners, what is the probability that at least two of them will order the same one?

3.. A doctor has found that 25% of her patients have eye problems, 10% have hearing problems, and 5% have both. Are the events "have eye problems" and "have hearing problems" independent? Justify your answer

4.. Explain the difference between mutually exclusive events and independent events using an example of each to illustrate your answer.

5.. Suppose you randomly draw two marbles, without replacement from a bag containing 6 green, 4 red and 3 black marbles

a) Draw a tree diagram to illustrate all possible outcomes of this draw

b) Determine the probability that both marbles are red

c) Determine the probability that you pick at least one green marble