An analyzer having an inner chassis surrounded by a housing includes sample and dilution probes, a mixing housing including first and second mixing chambers, a flow cytometer including a flow cell, and sample and sheath pumps configured to perform first and second pluralities of tasks, respectively. The first plurality of tasks includes: aspirating sample into the sample probe, dispensing sample from the sample probe into the first and second mixing chambers, delivering first sample-dilution fluid mixture to the flow cell, and delivering second sample-dilution fluid mixture to the flow cell. The second plurality of tasks includes: dispensing sheath to the flow cell in cooperation with the delivery of the first sample-dilution fluid mixture to the flow cell, and dispensing sheath to the flow cell in cooperation with the delivery of the second sample-dilution fluid mixture to the flow cell.