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PIMSO 2025 - Mathematics - Senior Secondary - National Round Question 10

PIMSO Maths · PIMSO 2025 - Mathematics - Senior Secondary - National Round

Question 10

The There are 16 different books to be placed on 3 labeled shelves: Shelf X, Shelf Y, and Shelf Z. The books must be arranged so that: Shelf Y holds 1 more book than Shelf X, Shelf Z holds 2 more books than Shelf Y, and each book is placed on exactly one shelf. In how many distinct ways can the books be distributed across the 3 shelves under these conditions?
  1. $\frac{16!}{4!5!7!}$
  2. $\frac{4!5!7!}{16!}$
  3. $4!5!7!$
  4. none