a fitness coach needs to use 3 different exercises from a list of 25 in a workout. how many different groups…

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, $n = 25$ and $r=3$.

Step2: Calculate factorial values

$n!=25! = 25\times24\times23\times22\times\cdots\times1$, $r!=3!=3\times2\times1$, and $(n - r)!=(25 - 3)!=22!=22\times21\times\cdots\times1$. Then $C(25,3)=\frac{25!}{3!(25 - 3)!}=\frac{25\times24\times23\times22!}{3\times2\times1\times22!}$.

Step3: Simplify the expression

Cancel out the $22!$ terms. We get $\frac{25\times24\times23}{3\times2\times1}$. $25\times24\times23 = 13800$ and $3\times2\times1=6$. Then $\frac{13800}{6}=2300$.

Answer:

2300