B737-300 ARRIVING DEN IS GIVEN VECTORS TO INTERCEPT ILS 35L WHEN THEY WERE TOLD TO EXPECT AND WERE SET UP FOR THE ILS 35R. ACFT WAS THEN VECTORED FOR ANOTHER APCH TO 35L.

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WHILE ENRTE TO DEN WE WERE ADVISED VIA ACARS OF DEN BEING A 2 RWY OP DUE TO 'STAFFING ISSUES' IN DEN. WE WERE TOLD THAT WE MIGHT BE SLOWED AND/OR HELD GOING INTO DEN. LUCKILY; I HAD UPLOADED SOME EXTRA FUEL. WE CONTINUED AND WERE SLOWED TO 240 KTS APPROX 150 NM OUT. WE CONTINUED IN AND WERE PROGRESSIVELY DSNDED ON THE DANDD ARR. AROUND DANDD WE WERE VECTORED W AND DSNDED TO 13000 FT MSL. WE WERE TOLD TO EXPECT RWY 35R. WE SET UP AND BRIEFED AN APCH TO RWY 35R. IT WAS NIGHT AND WE WERE IMC. 2 CTLRS LATER; AS WE WERE BEING VECTORED TO FINAL; WHEN WE WERE APPROX 7 MI FROM THE FAF WE WERE GIVEN OUR APCH CLRNC. THE CTLR GAVE A STANDARD TYPE CLRNC THAT INCLUDED A HDG; MINIMUM ALT UNTIL ESTABLISHED AND THEN 'CLRED FOR ILS RWY 35L.' AS WE USUALLY ARE DURING THAT PHASE OF FLT; OUR COCKPIT WAS BUSY WITH ACFT CONFIGN AND CHKLISTS -- THE FREQ WAS BUSY ALSO WITH NUMEROUS ARRIVING ACFT. TRIPLE SIMULTANEOUS ILS APCHS WERE BEING CONDUCTED. I READ BACK THE CLRNC AND HESITATED AT THE '35L' PART. I ASKED MY COPLT IF WE WERE ON THE L OR THE R. SHE REPLIED ON THE R. I ASKED THE CTLR WHAT RWY WE WERE CLRED FOR; HE RESPONDED THAT WE WERE CLRED FOR THE ILS RWY 35L. AT THAT TIME I SAID WE WERE NOT SET UP FOR THE L AND HE CLBED US AND VECTORED US IN A BOX PATTERN TO SET US UP FOR THE ILS RWY 35L. WE SCRAMBLED TO GET SET UP AND BRIEF THE NEW APCH. WE WERE VECTORED AND FLEW THE ILS RWY 35L WITH AN UNEVENTFUL LNDG. IF I HAD JUST SAID 'CLRED FOR THE APCH;' AND CONTINUED FOR RWY 35R; OR IF MY READBACK HAD BEEN STEPPED ON; WOULD THERE HAVE BEEN A 'CONFLICT?' WHAT IF I HAD ACCEPTED AN ACFT WITH AN INOP TCAS? OR SOME OTHER ACFT HAD INOP TCAS. HOW WOULD HAVING 2 OR 3 ACFT RESPONDING TO RA'S HAVE IMPACTED THAT OP? AT NIGHT AND IMC. I KNOW MYSELF AND MY FO WERE BOTH FATIGUED AND I HAVE TO WONDER IF TRACON WAS FATIGUED ALSO. WHAT WAS THE STAFFING ISSUE?