A company stores products in a warehouse. Storage bins in this warehouse are…
2021
A company stores products in a warehouse. Storage bins in this warehouse are specified by their aisle, location in the aisle, and self. There are 50 aisles, 85 horizontal locations in each aisle, and 5 shelves throughout the warehouse. What is the least number of products the company can have so that at least two products must be stored in the same bin?
- A.
251
- B.
426
- C.
4251
- D.
21251
Attempted by 187 students.
Show answer & explanation
Correct answer: D
Key idea: use the pigeonhole principle.
Compute the total number of distinct storage bins by multiplying the three choices (aisle, location in aisle, shelf):
50 × 85 × 5 = 21,250 bins.
By the pigeonhole principle, to guarantee at least two products are stored in the same bin you need one more than the number of bins.
Therefore, the least number of products required is 21,250 + 1 = 21,251.
Answer: 21,251
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