a typical platoon consists of 20 soldiers. if there are 28 soldiers available to create a platoon, how many…

Explanation:

Step1: Identify combination formula

The problem is about combinations. 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, $n = 28$ and $r=20$. Since $C(n,r)=C(n,n - r)$, we can use $C(28,20)=C(28,28 - 20)=C(28,8)$ for easier calculation.

Step2: Calculate factorial values

$n!=n\times(n - 1)\times\cdots\times1$. So, $28! = 28\times27\times\cdots\times1$, $8! = 8\times7\times\cdots\times1$, and $(28 - 8)!=20! = 20\times19\times\cdots\times1$. Then $C(28,8)=\frac{28!}{8!(28 - 8)!}=\frac{28!}{8!×20!}=\frac{28\times27\times26\times25\times24\times23\times22\times21}{8\times7\times6\times5\times4\times3\times2\times1}$.

Step3: Simplify the expression

$\frac{28\times27\times26\times25\times24\times23\times22\times21}{8\times7\times6\times5\times4\times3\times2\times1}=3108105$.

Answer:

$3108105$