Joey throws a dice 3 times and decides to invite the same number of guests for his birthday party as the sum of the outcomes of the throws. What’s the probability that he invites 12 guests? Pick one.
A) 1/6  B) 1/16  C) 1/18  D) 1/36  E) 25/216
Total outcomes:   6^3.   Favorable outcomes:   {6 - 5 - 1} - 6 cases ({6 - 5 - 1}, {6 - 1 - 5} , {5 - 6 - 1}, {5 - 1 - 6}, {1 - 6 - 5}, {1 - 5 - 6});   {6 - 4 - 2} - 6 cases;   {6 - 3 - 3} - 3 cases;   {5 - 5 - 2} - 3 cases;   {5 - 4 - 3} - 6 cases;   {4 - 4 - 4} - 1 case.   6 + 6 + 3 + 3 + 6 + 1= 
<gadget id="calculator">6 + 6 + 3 + 3 + 6 + 1</gadget>
<output>25</output>
25.   P= (favorable)/(total) = 25/6^3.   Answer: 25/216.
<result>E</result>
Joey throws a dice 3 times and decides to invite the same number of guests for his birthday party as the sum of the outcomes of the throws. What’s the probability that he invites 12 guests?