Jean puts 12 books on a shelf in random order. Three are by the same author. What is the probability that those 3 books will be next to each other? it's one of these...
4.55%
8.33%

4.55

Step-by-step explanation:

AEight different books were put on a shelf in random order. Calculate probability that two specific books were put near each other.

My Let's divide the space on the shelf into eight slots. Let's also name our two books, "A" and "B" respectively. We have two sets of combinations - in the first set of combinations we have AB (i.e. A goes first). For example, A is put into the first slot and B is put into the second slot. Next example, A is put into the second slot and B is put into the third slot. And so on. There are 7 such AB combinations in total. By the same logic there are also 7 BA combinations. Obviously there is no overlap between said combinations, thus we can sum them up and get 14 combinations in total where books A and B are put side by side.

As for number of total combinations of books on the bookshelf, it's equal to "n!", where n is equal to 8. Why? Because in order to calculate combinations when repetitions are forbidden and order is important we use this formula:

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step-by-step explanation:

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