Question

Probability help!!!!!!!!!! Medal!

Adrian's CD player can hold six disks at a time and shuffles all of the albums and their songs. If he has thirteen CD's, how many different combinations of six CD's can he put in the player?

Answer 1

@KamiBug @ganeshie8 @paki

Answer 2

13 objects are there you want to choose 6 from them

Answer 3

@sleepyjess

Answer 4

Yeah but I need to know how many different possibilities are there to be put into the cd player.

Answer 5

Total number of ways of choosing 6 objects from 13 objects:

Answer 6

sorry hard to draw with a laptop haha ;)

Answer 7

Its okay. I dont get it though lol

Answer 8

There are 13 CDs. Let's say there are 6 slots to fit these 13 CDs:
\[\underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \]
In the first slot, we have all 13 CDs available to us, so we can choose from all 13 for the first slot:
\[\underline{13} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \]
For the second slot, we have 12 CDs to choose from (we've already chosen a CD for the first slot and we cannot reuse that one).
\[\underline{13} \ \ \underline{12} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \underline{\hspace{0.5cm}} \ \ \]
We can continue down, subtracting from the pool of total CDs we have until we fill up all 6 slots. We then multiply through to get our answer, which is the same as what @Here_to_Help15 is suggesting.

Answer 9

Okay, multiply by what?

Answer 10

@katkipe can you simplify?

Answer 11

I know ya can hun :P

Answer 12

Right........I dont know wth you are asking me to simplify though.

Answer 13

So from the intermediate work that I typed up, it would be \(13 \times 12 \times \ldots\). You should fill in the remaining 4 slots and that would give you your answer.

Answer 14

With any numbers or from descending order?

Answer 15

One sec :)

Answer 16

No. Read what I typed up. Do you see how I got \(13\) and \(12\) for the first two slots?

Answer 17

Simplifu that hun sorry i couldnt draw it out its kinda hard to with laptop :p

Answer 18

Right. That is NOT my question. I am asking do I put 13, 12, 11, 10, 9 or 13, 6, 4 and so on?

Answer 19

Okay. Thanks.

Answer 20

The first option: you would put in \(13, 12, 11, \ldots\) until you fill in all six slots.

Answer 21

Okay. That's more helpful.

Answer 22

O.o i feel like a retard D:

Answer 23

If you simplify the combination formula that @Here_to_Help15 posted, you will see that you get the same equation, namely \[\frac{13!}{7!}\] which I'm assuming is what @Here_to_Help15 wanted it to simplify to or wanted you to see.

Answer 24

yes ;) but i dont know i am confused now :p

Answer 25

Thank you both.