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: Identify the problem type

This is a combination problem where we need to find the number of ways to choose 3 exercises from 25, which is calculated using the combination formula \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 25 \) and \( k=3 \).

Step2: Calculate the factorial values

First, calculate \( n!=25! = 25\times24\times23\times22! \), \( k!=3!=3\times2\times1 = 6 \), and \( (n - k)!=(25 - 3)!=22! \).

Step3: Substitute into the combination formula

\( C(25,3)=\frac{25!}{3!(25 - 3)!}=\frac{25\times24\times23\times22!}{6\times22!} \)

Step4: Simplify the expression

Cancel out the \( 22! \) terms, then calculate \( \frac{25\times24\times23}{6} \). First, \( 25\times24 = 600 \), then \( 600\times23=13800 \), and \( \frac{13800}{6}=2300 \).

Answer:

2300