In each part below, just write the answer as a math expression. You don't have to find the numerical values. But please make sure there are not infinite sums in your answers.

a)18 dice are rolled. Find the chance that two of the faces appear 5 times each, another two faces appear 3 times each, and the remaining two faces appear 1 time each.

b)Repeat Partain the case when the number of dice rolled isn't 18 but is instead a random number that has the Poisson(18)

(18)distribution.

c)As in Partb, roll a random number of dice, where the random number has a Poisson(18)distribution. Don't touch any die that shows the face with six spots. If there are any other dice (that is, if there are dice that don't show six spots), roll those dice one more time. Then stop.

LetSbe the total number of dice that show the face with six spots when you stop. Find the distribution ofS.