Twelve science books

Probability Level 3

There are 12 different science books on the same shelf. Five of them are about mathematics, four of them about physics and three of them about chemistry. Find the probability of the event that all mathematics books are together, all physics book are together and all chemistry books are together. Given that the probability can be expressed as 1/N, what is the value of N?


The answer is 4620.

Paul Fournier by Paul Fournier , 70, Canada

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2 solutions

Nguyen Thanh Long
Aug 10, 2015

It is very easy to see that: the number of permutations of books when they are in order is: S = 3 ! × 5 ! × 4 ! × 3 ! S=3! \times 5! \times 4! \times 3! So N is result of the formula: 12 ! S = 4620 \frac{12!}{S}=\boxed{4620}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Since there are 12 different books, there are 12! ways of arranging them. If we group them by subject matter, there are 5! ways to arrange the math books, 4! ways to arrange the physics books and 3! ways to arrange the chemistry books. On top of that, there are 3! ways each group can be arranged collectively. Hence, the P( all same subject matter books are together)= 3! * (( 5! 4! 3!)/(12!))=1/4620

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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