Question

A bag contains 5 red marbles and 8 yellow marbles. You are asked to draw 3 marbles from the bag without replacement. In how many ways can you draw 2 reds and 1 yellow?

Answer 1

\[\dbinom{5}{2}\times \dbinom{8}{1}\]

Answer 2

which is really not an answer, it just restates the question. the answer is to compute these

Answer 3

this just says "the number of ways to choose 2 from 5 times the number of way to choose 1 from 8" so there is no real information here. now we compute

Answer 4

ohhhh, so it's back to using the binomial expressions thing, or whatever it's called

Answer 5

\[\dbinom{5}{2}=\frac{5\times 4}{2}=10\]
\[\dbinom{8}{1}=8\] in your head

Answer 6

so you get 80

Answer 7

\[\left(\begin{matrix}5 \\ 2\end{matrix}\right) =10\]

Answer 8

finally i was right! yes!!

Answer 9

for the first one anyways

Answer 10

yeah it is that. don't forget
\[\dbinom{n}{k}\] reads "n choose k" so it literally means the number of ways to choose k things from a set of n

Answer 11

ok, thanks a bunch (again!). i'm starting to understand this thing they call "math" now, haha