Question

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?

Answer 1

its on permutations and combinations algebra 2

Answer 2

@Preetha

Answer 3

@mathstudent55 ???

Answer 4

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

Answer 5

how do i do it?

Answer 6

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

Answer 7

brb

Answer 8

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.

Answer 9

eek i got a weird answer

Answer 10

what did you get?

Answer 11

\[11/18144\]

Answer 12

that was evaluating the right side

Answer 13

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.

Answer 14

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

Answer 15

i got 220

Answer 16

is that for the first dinner

Answer 17

yes

Answer 18

ok how do i find the others

Answer 19

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.

Answer 20

not sure how to solve that?

Answer 21

its 9/3??

Answer 22

Check my answer, I generalized the formula for you

Answer 23

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

Answer 24

i got 84

Answer 25

yeah, probably, I didn't calculated

Answer 26

ok 3rd?

Answer 27

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

Answer 28

6

Answer 29

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

Answer 30

mm let me see ill try

Answer 31

i got 20

Answer 32

yes. I think

Answer 33

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

Answer 34

yes, you have learned ;)

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

yes :)

Answer 39

oh haha okay thank you so much (:

Answer 40

Anytime ;)