Question

A bag has 2 red marbles, 3 blue marbles and 5 white marbles. A marble is
randomly selected and then placed back in the bag. You do this 8 times. What is
the probability of choosing 1 red marble, 3blue marble and 4 white marbles?

Answer 1

add up all the marbles to get 10
you then create fractions to represent the probability of getting each colored marble from the bag

so you have 2/10 for red 3/10 for blue and 5/10 for white

next you can just create a tree diagram

Answer 2

n=number of marbles (10)
r=number of red marbles (2)
b=number of blue marbles (3)
w=number of white marbles (5)
\(p_r\) = probability of drawing a red (2/10)
\(p_b\) = probability of drawing a blue (3/10)
\(p_w\) = probability of drawing a white (5/10)

Use the multinomial distribution (see - http://en.wikipedia.org/wiki/Multinomial_distribution#Probability_mass_function )
Here is the probability for your problem
$$
\large
{n!\over r!b!w!}\times (p_r)^1(p_b)^3(p_w)^5
$$

Does this make sense?