# Thread: Permutations and Combinations in Probability

1. ## Permutations and Combinations in Probability

Hi, can someone please explain what to do, stats really isn't my thing, so if you could please explain your answer, I'd really appreciate it!

3 red cubes, 4 blue, 6 yellow are arranged in a row. find the probability that (a) the cubes at each end are the same color
and (b) the cubes at each end are of a different color.

Thanks a lot!

2. Originally Posted by overduex
Hi, can someone please explain what to do, stats really isn't my thing, so if you could please explain your answer, I'd really appreciate it!
3 red cubes, 4 blue, 6 yellow are arranged in a row. find the probability that (a) the cubes at each end are the same color
The total number of ways the arrange thes cubes is $N=\frac{13!}{(3!)(4!)(6!)}$ that becomes your denominator.
The number of ways to have a reds at each end is $\frac{11!}{(1!)(4!)(6!)}$

Now you do it for the other two colors.

3. Originally Posted by Plato
The total number of ways the arrange thes cubes is $N=\frac{13!}{(3!)(4!)(6!)}$ that becomes your denominator.
The number of ways to have a reds at each end is $\frac{11!}{(1!)(4!)(6!)}$

Now you do it for the other two colors.
after you do it for the other 2 colors, do you multipy them together? or add?

4. Originally Posted by overduex
after you do it for the other 2 colors, do you multipy them together? or add?

5. Originally Posted by Plato
sorry to bother again, but could you explain how to get the answer?
It is supposed to be 4/13 but i keep getting ridiculous numbers as answers. I basically just added what you had written
11!/(1!)(4!)(6!) + 11!/(3!)(2!)(6!) + 11!/(3!)(4!)(4!)

do you see anything I may be doing wrong?

6. Iunno whats wrong. I tried it out, I i seemed to get 4/13. Maybe you're simplifying wrong?

11!/(1!x4!x6!) = 2310

11!/(3!x2!x6!) = 4620

11!/(3!x4!x4!) = 11550

13!/(3!x4!x6!) = 60060

So, (2310/60060) + (4620/60060) + (11550/60060) = (18480/60060) = (4/13).

If your entering the numbers into your calculator like this 11!/3!x4!x4!, then you might be getting the wrong answer, be in reality it'd be this:
(11!/3!) x 4! x 4! which might explain the random numbers.

Iunno whats wrong. I tried it out, I i seemed to get 4/13. Maybe you're simplifying wrong?

11!/(1!x4!x6!) = 2310

11!/(3!x2!x6!) = 4620

11!/(3!x4!x4!) = 11550

13!/(3!x4!x6!) = 60060

So, (2310/60060) + (4620/60060) + (11550/60060) = (18480/60060) = (4/13).

If your entering the numbers into your calculator like this 11!/3!x4!x4!, then you might be getting the wrong answer, be in reality it'd be this:
(11!/3!) x 4! x 4! which might explain the random numbers.

yeah, I figured out my mistake. I was wayyy off. haha, thanks for trying though!