MEDAL FAN AND TESTIMONIAL:on a camping trip you bring 12 items for 4 dinners for each dinner you use 3 items in how many ways can you choose the 3 items for the first dinner? for the second? for the third? for the fourth?

- anonymous

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- anonymous

its on permutations and combinations algebra 2

- anonymous

@Preetha

- anonymous

@mathstudent55 ???

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## More answers

- anonymous

It is combinations. And the result is same for the all four dinners.

- anonymous

how do i do it?

- anonymous

I can do the problems that are already set up but not word problems where i have to set it up

- anonymous

brb

- anonymous

You have four dinner. And for all of them, you need to make a decision to pick 3 items among 12 items. So 3 combinations among 12 item is:
\[\left(\begin{matrix}12 \\ 3\end{matrix}\right) = \frac{ 12 \times 11 \times 10 }{ 9! \times 3! }\]
I had a mistake though, in my first statement, where I said that they were equal. It is not.
If you pick 3 items among 12, you will have 9 items left, since you took 3 of them.

- anonymous

eek i got a weird answer

- anonymous

what did you get?

- anonymous

\[11/18144\]

- anonymous

that was evaluating the right side

- anonymous

ohh sorry, I forgot to add factorial sign to the 12.
It is like this:
\[\frac{ 12! }{ 9! \times 3! }\]
it is originally this way.

- anonymous

The general formula is:
\[\left(\begin{matrix}c \\ n\end{matrix}\right) = \frac{ c! }{ n! \times (c - n)! }\]

- anonymous

i got 220

- anonymous

is that for the first dinner

- anonymous

yes

- anonymous

ok how do i find the others

- anonymous

For the second dinner you will calculate this:
\[\left(\begin{matrix}9 \\ 3\end{matrix}\right)\]
Since we took the first three items, 9 left in the item list.

- anonymous

not sure how to solve that?

- anonymous

its 9/3??

- anonymous

Check my answer, I generalized the formula for you

- anonymous

\[\left(\begin{matrix}c \\ n\end{matrix}\right) = \frac{c!}{n! \times (c-n)!}\]

- anonymous

i got 84

- anonymous

yeah, probably, I didn't calculated

- anonymous

ok 3rd?

- anonymous

How many items do we left? We used 6 of them so far right?

- anonymous

6

- anonymous

yes, you will chose 3 from 6. Use the formula that I gave you. Did you understand how to use the formula?

- anonymous

mm let me see ill try

- anonymous

i got 20

- anonymous

yes. I think

- anonymous

ok for the fourth then all of the variables in the formula you gave are 3 right

- anonymous

yes, you have learned ;)

- anonymous

i think so but the problem is that I'm getting 1/6?

- anonymous

you should get 1. Check if you didn't make any calculation mistakes.

- anonymous

or i guess i would just say one because there isn't anything left

- anonymous

yes :)

- anonymous

oh haha okay thank you so much (:

- anonymous

Anytime ;)

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