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Probability question combinatorial mathematics?
Eight different book, three in physics and five in electrical engineering, are placed at random on a library shelf. What is the probability that the three physics books are all together?
I have the answer; its 3/28
i have no idea how it is actually 3/28 anyone wanna clarify this?
thank you :)
Hey lhurlbert.
If all the three books together then it means that you can look at each combination as "sliding" along for each possibility.
You have 8 books in total which means if you start all books at the left-most side you get 6 possibilities where the books start at positions 1,2,3,4,5 and 6.
Now we need to find the number of possibilities of re-arranging the books and for this we use a standard combinatoric identity.
The number of ways arranging 8 books given 5 engineering books (or 3 physics books) is 8C5 = 8C3 or using R:
> choose(8,5)
[1] 56
> choose(8,3)
[1] 56
So the total number of possibilities is 6/56 = 3/28 as expected.
Hello, lhurlbert!
Quote:
Eight different book, 3 in Physics and 5 in Electrical Engineering, are placed at random on a shelf.
What is the probability that the three Physics books are all together?
Answer: 3/28
There are: .possible orders.
Duct-tape the 3 Physics books together.
They can be ordered inways.
We have 6 "books" to arrange: .
They can be ordered inways.
Hence, the 8 books can be ordered inways.
Therefore, the probability is: .