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?
$_{10}c_{4} = \frac{10!}{(10-4)!4!}$
○ 210
○ 1,260
○ 6,300
○ 25,200

Explanation:

Step1: Recall combination formula

The formula for combinations is $_{n}C_{r} = \frac{n!}{(n-r)!r!}$, where $n=10$, $r=4$.

Step2: Substitute values into formula

$_{10}C_{4} = \frac{10!}{(10-4)!4!} = \frac{10!}{6!4!}$

Step3: Expand factorials and simplify

$\frac{10\times9\times8\times7\times6!}{6!\times4\times3\times2\times1} = \frac{10\times9\times8\times7}{4\times3\times2\times1}$

Step4: Calculate the final value

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

Answer:

210