Thread: grouped probabilities

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!

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 in ways.

We have 6 "books" to arrange: .
They can be ordered in ways.

Hence, the 8 books can be ordered in ways.


Therefore, the probability is: .