Question

You win a prize at a carnival. You can pick 5 prizes off the first shelf, 3 prizes off the second shelf, or 1 prize off the third shelf. You decide to take the first shelf option. If there are 10 different prizes on the first shelf, how many ways can you select your prizes? A. 252 B. 50 C. 100,000 D. 30,240

Answer 1

you are being asked how many ways to choose 5 from a set of 10
this is written as
\[\binom{10}{5}\] or sometimes
\[_{10}C_5\] or even
\[^{10}C_5\]
read "ten choose 5"
and computed via
\[\binom{10}{5}=\frac{\overbrace{10\times 9\times 8\times 7\times 6}^{\text{5 terms}}}{5\times 4\times 3\times 2}\]

Answer 2

cancel first, multiply last, since the answer is a whole number
or else use a calculator, most have this button
in wolfram just type in "ten choose 5" and you will get the answer