Question

a dance instructor chose four of his 10 students to be on stage for a performance. if order does not matter, in how many different ways can the instructor choose the four students?
$_{10}c_4 = \frac{10!}{(10 - 4)!4!}$

Explanation:

Step1: Recall combination formula

$C(n,k)=\frac{n!}{(n-k)!k!}$ where $n=10,k=4$

Step2: Substitute values

$C(10,4)=\frac{10!}{(10-4)!4!}=\frac{10!}{6!4!}$

Step3: Simplify factorials

$\frac{10×9×8×7×6!}{6!×4×3×2×1}=\frac{10×9×8×7}{4×3×2×1}$

Step4: Calculate result

$\frac{5040}{24}=210$

Answer:

210