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How many ways can 6 different books be placed on a shelf if the only dictionary must be on the left end?

User Agomcas
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Final answer:

There are 120 ways to arrange 6 different books on a shelf with the dictionary on the left end because the remaining 5 books can be arranged in any order, resulting in 5 factorial (5!) possibilities.

Step-by-step explanation:

The question asks how many ways 6 different books can be placed on a shelf if the dictionary must be on the left end. Since one position is already fixed for the dictionary, we are left with 5 books to arrange. The remaining 5 books can be arranged in any order, which gives us 5! (5 factorial) possibilities. A factorial is found by multiplying a series of descending natural numbers. Therefore, 5! equals 5 × 4 × 3 × 2 × 1, which is 120. So, there are 120 ways to arrange the remaining books on the shelf with the dictionary at the left end.

User Simon Bruneaud
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