The phrase "a third assignment" is correct and usable in written English.
You can use it when referring to the third task or piece of work in a series of assignments.
Example: "After completing the first two assignments, I am now ready to tackle a third assignment that has been given to us."
Alternatives: "the third task" or "the third piece of work".
Dwek promised that he could infiltrate his own Syrian Jewish community, but Christie and his prosecutors gave Dwek a second assignment: exposing political corruption.
She photographed the first story I published, although I didn't meet her in person until a second assignment, which took us to the waterfront on Staten Island, where I had been following a teen-age girl who lived on the street.
As a first assignment, Mr. Caulfield sent Mr. Ulasewicz to Chappaquiddick, Mass., to find out exactly what Senator Edward M. Kennedy had been doing on the night in 1969 when Mary Jo Kopechne, a former campaign aide, drowned after the car in which they were riding plunged off a bridge.
Though, when students are required to hand-in a first assignment, completion rate jumps to 45%.
The results of multi-detection allowed a first assignment of the differently detectable bands to particular chemical substance classes (e.g., lipophilic components), enabled the comparison of different commercially available pigment batches and revealed substantial variations in the composition of the batches.
Rousey has yet to do the same, and Nunes is a stiff order for a first assignment back to redemption.
The mass spectrum of intact H2A histones allowed a first assignment of six potential isoforms in the first peak.
A second assignment test was made examining only the four coat-color/size groups of small poodles.
A second assignment at 06.00 hours (before the end of the night shift) asked the critical care nurse to remove the earplugs from the patient and to keep them in the closed canister again.
A second assignment was created based on preliminary data collected from Spring 2013, which indicated that nearly all students were willing to modify their study plans in some way.
