$$Question: How many ways are there to distribute 4 distinct chemical samples into 2 identical storage containers such that each container has at least one sample?

Sun, 03 May 2026 17:13:25 +0000

Title: How Many Ways to Distribute 4 Distinct Chemical Samples into 2 Identical Containers with At Least One Sample Each? When working with discrete objects like chemical samples and containers with unique constraints, combinatorics becomes both essential and fascinating. One common yet cleverly non-trivial problem is: How many ways can you distribute 4 distinct chemical samples into 2 identical storage containers, ensuring that no container is empty? This problem lies at the intersection of combinatorics and logistics—particularly relevant in laboratories, supply chains, and quality control scenarios. Let’s unpack the solution step-by-step to uncover how many valid distributions satisfy the condition that each container holds at least one sample, and the containers themselves cannot be told apart. ---