Question: 2018 Fall Midterm - 4
Elisa Kazan's neighborhood pub serves 8 different types of cider; denote these types by $C_1,C_2,\dots,C_8$.
Elisa invites 7 friends to this pub and orders one cider for each friend. Different
friends may get the same type of cider. (Elisa came by car and, therefore, orders a glass of water
for herself.)
In how many ways can Elisa place these orders of cider, such that exactly 4 of her friends get a cider of type $C_3$?
In how many ways can Elisa place these orders of cider, such that exactly 4 of her friends get a cider of type $C_3$?
(a)
${7 \choose 4} \cdot 8^4$
(b)
${7 \choose 4} \cdot 8^3$
(c)
${7 \choose 4} \cdot 7^4$
(d)
${7 \choose 4} \cdot 7^3$