Rather than study for math, you and your buddies decide to get together for a marathon movie-watching popcorn-gorging event on Saturday night. You decide to watch four movies selected at random from the list. How many sets of four movies are possible $$\begin{array} { | c | c | }
\hline \text { Name } & \text { Revenue (\$ million) } \
\hline \text { The Grudge } & \$ 9.24 \
\hline \text { Ray } & \$ 6.54 \
\hline \text { The Forgotten } & \$ 6.01 \
\hline \text { Friday Night Lights } & \$ 5.99 \
\hline \text { Cellular } & \$ 5.85 \
\hline \text { Shall We Dance } & \$ 5.82 \
\hline \text { The Village } & \$ 5.58 \
\hline \text { AVP: Alien Vs. Predator } & \$ 5.46 \
\hline \text { Catwoman } & \$ 5.10 \
\hline \text { Sky Captain and the World of } \
\text { Tomorrow } & \$ 5.09 \
\hline
\end{array}$$
A) 5,040 sets
B) 210 sets
C) 720 sets
D) 182 sets
E) 91 sets

Question

Rather than study for math, you and your buddies decide to get together for a marathon movie-watching popcorn-gorging event on Saturday night. You decide to watch four movies selected at random from the list. How many sets of four movies are possible    $$\begin{array} { | c | c | } 
\hline \text { Name } & \text { Revenue (\$ million) } \
\hline \text { The Grudge } & \$ 9.24 \
\hline \text { Ray } & \$ 6.54 \
\hline \text { The Forgotten } & \$ 6.01 \
\hline \text { Friday Night Lights } & \$ 5.99 \
\hline \text { Cellular } & \$ 5.85 \
\hline \text { Shall We Dance } & \$ 5.82 \
\hline \text { The Village } & \$ 5.58 \
\hline \text { AVP: Alien Vs. Predator } & \$ 5.46 \
\hline \text { Catwoman } & \$ 5.10 \
\hline \text { Sky Captain and the World of } \
\text { Tomorrow } & \$ 5.09 \
\hline
\end{array}$$
A) 5,040 sets
B)  210 sets
C)  720 sets
D)  182 sets
E)  91 sets

Quizplus · Accepted Answer

The total number of movies listed is 10. The number of ways to select 4 movies out of 10 is calculated using the combination formula, which is $C(n, k) = \frac{n!}{k!(n-k)!}$. Substituting $n=10$ and $k=4$, we get $C(10, 4) = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$. Therefore, there are 210 possible sets of four movies.

Rather Than Study for Math, You and Your Buddies Decide