Question

I have no clue how to figure this out. Please help and work through it.

How many combinations of 5 students can a teacher choose from 24 students?


A.
120


B.
42,504


C.
5,100,480


D.
7,962,624

Answer 1

I think it's C but that's a educated guess.

Answer 2

you are being asked for "24 choose 5" written as
\[\binom{24}{5}\] so sometimes
\[_{24}C_5\] or even \[^{24}C_5\] and computed via
\[\frac{\overbrace{24\times 23\times 22\times 21\times 20}^{\text{ 5 terms}}}{5\times 4\times 3\times 2}\] cancel first multiply last

Answer 3

or just cheat
http://www.wolframalpha.com/input/?i=24+choose+5

Answer 4

its B lol

Answer 5

\[\left(\begin{matrix}24 ! \\5! * (24-5)! \end{matrix}\right)\]