On a shelf, there are 10 books, which include 3 paperback books and 7 hardback books. If 5 books are chosen at random without replacement, how many different combinations are there such that at least one paperback book is included?

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229

230

231

Correct

232

233

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Official Explanation

Official

To determine the number of combinations that include at least one paperback book, we can use the approach of calculating the total combinations and subtracting the combinations that include no paperback books. The total number of ways to select 5 books from 10 is given by…

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Comments

YuMar 19, 2025

got this wrong on my practice

therealneytvMay 25, 2024

Thank you very much!

What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.