Question

a fitness coach needs to use 3 different exercises from a list of 25 in a workout. how many different groups of 3 exercises can she choose? enter the answer in the box. groups

Explanation:

Step1: Identificar fórmula de combinaciones

Utilizamos la fórmula de combinaciones $C(n,r)=\frac{n!}{r!(n - r)!}$, donde $n$ es el total de elementos y $r$ es el número de elementos a elegir. Aquí, $n = 25$ y $r=3$.

Step2: Calcular factoriales

$n!=25!$, $r!=3!$ y $(n - r)!=(25 - 3)!=22!$. Entonces $C(25,3)=\frac{25!}{3!(25 - 3)!}=\frac{25!}{3!×22!}$.
Como $25! = 25\times24\times23\times22!$, entonces $C(25,3)=\frac{25\times24\times23\times22!}{3!×22!}$.

Step3: Simplificar y calcular

$3!=3\times2\times1 = 6$. Entonces $C(25,3)=\frac{25\times24\times23}{6}$.
$25\times24\times23=25\times552 = 13800$. Y $\frac{13800}{6}=2300$.

Answer:

2300