Question: 2018 Winter Final - 24
Elisa Kazan has successfully completed her second year as President of the Carleton Computer Science Society.
In order to celebrate this, Elisa throws a party. She invites 15 students; thus, the total number of students
at the party is equal to 16. Elisa has brought an unlimited amount of drinks: 5 types $C_1,C_2,C_3,C_4,C_5$
of cider and 3 types $B_1,B_2,B_3$ of beer. Each of the 16 students gets 3 drinks; each of these drinks is
uniformly, and independently, chosen from the 8 types of drinks.
Define the following random variable $X$:
Hint: Use indicator random variables.
Define the following random variable $X$:
- X = the number of students who get exactly 2 ciders.
Hint: Use indicator random variables.
(a)
$2^{4} \cdot 3^{2} \left. \cdot 5^{2} \middle/ 8^{3} \right.$
(b)
$2^{4} \cdot 3^{2} \cdot \left. 2^{5} \middle/ 8^{3} \right.$
(c)
$2^{4} \cdot 3^{2} \cdot \left. 5^{2} \middle/ 3^{8} \right.$
(d)
$3^{2} \cdot \left. 5^{2} \middle/ 8^{3} \right.$