Question: 2018 Winter Midterm - 4
Let $b \geq 1$ and $c \geq 1$ be integers. Elisa Kazan's neighborhood pub serves $b$ different types
of beer and $c$ different types of cider. Elisa invites 6 friends to this pub and orders 7 drinks,
one drink (beer or cider) for each friend, and one cider for herself. Different people may get the
same type of beer or cider.
In how many ways can Elisa place these orders, such that exactly 4 people get a beer?
In how many ways can Elisa place these orders, such that exactly 4 people get a beer?
(a)
${6 \choose 4} \cdot b^{4} \cdot c^{2}$
(b)
${6 \choose 4} \cdot b^{4} \cdot c^{3}$
(c)
${7 \choose 4} \cdot b^{4} \cdot c^{3}$
(d)
None of the above.