Problem 23 · 2015 Math Kangaroo
Stretch
Counting & Probability
careful-counting
Petra has three different dictionaries and two different novels on her bookshelf. In how many different ways can she arrange the books, if all the dictionaries should stay together and likewise the novels as well?
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Answer: B — 24
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Hint 1 of 2
Treat the dictionaries as one block and the novels as another, then arrange the two blocks.
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Hint 2 of 2
Multiply: arrange the 2 blocks, then arrange within the 3-dictionary block and within the 2-novel block.
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Approach: block (glue) the groups, then count
- The 3 dictionaries form one block, the 2 novels another: 2! ways to order the two blocks.
- Inside: 3! ways for the dictionaries, 2! ways for the novels.
- Total = 2! × 3! × 2! = 2 × 6 × 2 = 24.
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