How many ways to choose 2 books out of 5?

Question

BlackTom AI · Accepted Answer

To determine the number of ways to choose 2 books from 5, we are counting combinations where order does not matter. 
Option a: 10. This matches the combination formula C(n, k) = n! / (k!(n-k)!), here C(5,2) = 5! / (2! 3!) = 10. 
Option b: 25. This would imply counting ordered pairs or using a mistaken multiplication like 5 × 5, which overcounts or ignores the non-repetition rule for choosing two distinct books. 
Option c: 5. This would correspond to choosing only one item or misapplying the idea of selecting without regard to the second choice. It ignores the possible second pick, so it’s too small. 
Option d: 20. This value can arise if someone mistakenly uses permutations (order matters) as if there were 5 × 4 = 20 ways to pick two books, which double-counts since the order of the two books does not matter in a simple “choose 2” problem.

In summary, the correct reasoning uses combinations, not permutations, and yields C(5,2) = 10, which aligns with option a.

How many ways to choose 2 books out of 5?单项选择题

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