Probability Problem, very confused!

[pratikf]

Hi, please tell me how to solve this problem.

4 mathematics and 5 physics books are arranged in a row on a shelf at random. Find the probability that the books on the same subject will be put together.

[khkr]

4 math books in 4! ways
5 physics books in 5! ways
now they can be arranged in 4!*5!*2 ways

[rashmi]

I too agree with the above solution.

[serg14]

We have the permutations of 9 elements: 4 of one kind and 5 of another.
The number of total variants: 9! / (4! * 5!) = 126.

The elements of the same kind will be put together in only 2 cases:
1) Physics books are aranged at the left and math ones at the right
2) Vice versa

Therefore, the probability = 2 / 126 = 1/63.

[rashmi]

well ,seems everyone here is right.I'll explain.

total no. of ways of arranging all 9 books= 9! =A
total no. of arranging books such that all books of one kind are together
= 4! * 5! * 2 = B

thus probabilty that all books of one kind are together = B/A

[Econ]

As serg14 mentioned there are two cases: either the 4 maths first or the five phys books first. The probability for the first case is (4/9)(3/8)(2/7)(1/6)(1)(1)(1)(1)(1)=1/126 and for the second (5/9)(4/8)(3/7)(2/6)(1/5)(1)(1)(1)(1)=1/126. Total 2/126=1/63.