Question

movie selections the foreign language club is showing a four - movie marathon of subtitled movies. how many ways can they choose 4 from the 19 available? there are ways to choose 4 from the available 19 movies.

Explanation:

Step1: Identify combination formula

The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items, and $r$ is the number of items to be chosen. Here $n = 19$ and $r=4$.

Step2: Calculate factorial values

$n!=19! = 19\times18\times17\times16\times15\times\cdots\times1$, $r!=4!=4\times3\times2\times1$, and $(n - r)!=(19 - 4)!=15!=15\times14\times\cdots\times1$. Then $C(19,4)=\frac{19!}{4!(19 - 4)!}=\frac{19!}{4!×15!}=\frac{19\times18\times17\times16\times15!}{4\times3\times2\times1\times15!}$.

Step3: Simplify the expression

Cancel out the $15!$ terms. We have $\frac{19\times18\times17\times16}{4\times3\times2\times1}$. $19\times18\times17\times16=93024$ and $4\times3\times2\times1 = 24$. Then $\frac{93024}{24}=3876$.

Answer:

3876