WDB BEING VECTORED FOR VISUAL APCH TO DTW THOUGHT THEY WERE CLRED FOR RWY 21R. ATC GAVE TFC INFO ON A DC8 FOR RWY 21R AND TOLD THE WDB TO FOLLOW AN A320 FOR RWY 21L. DUE TO CONFUSION ON WHICH RWY THE WDB WAS CLRED TO THEY OVERSHOT RWY 21L FINAL AND GOT IN CLOSE PROX TO THE DC8. WHEN THE TWR CTLR CLRED THEM TO LAND RWY 21L AND THEY GOT LINED UP THEY HAD TO MAKE A GAR AS THE A320 WAS STILL IN THE RWY.

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ON OUR APCH TO DTW THE CAPT WAS HAND FLYING THE AIRPLANE. WE HAD BEEN ADVISED BY APCH CTL TO EXPECT RWY 21R AND THIS WAS WHAT WE BRIEFED. WE WERE ON A HDG OF 280 DEGS DSNDING TO 4000 FT. APCH POINTED OUT DC8 TFC 3 O'CLOCK AND 2 MI DSNDING TO 3000 FT. AT THAT POINT THE DC8 WAS BELOW US AND SLIGHTLY BEHIND. WE GUESSED THAT IT WAS PROBABLY GOING TO WILLOW RUN ARPT. WE WERE GIVEN NEW HDGS OF 250 DEGS AND THEN 230 DEGS. APCH POINTED OUT A320 TFC AHEAD OF US ON A L BASE. WHEN WE SAID WE HAD THE TFC IN SIGHT THEY SAID THAT WE WERE CLRED FOR THE VISUAL APCH AND FOLLOW THE A320 TO THE ARPT. NO MENTION WAS MADE OF A DIFFERENT RWY. THE A320 OVERSHOT BOTH RWY 21L AND RWY 21C AND APPEARED TO BE HEADED TO RWY 21R THEN HE CONTINUED A L TURN TO GO BACK TO RWY 21L. AT ABOUT THIS TIME WE GOT THE TCASII CLB ADVISORY AND THE CAPT STARTED AN IMMEDIATE CLB. APCH CTL THEN GAVE US AN IMMEDIATE L TURN TO HDG 180 DEGS. AT THAT POINT THE DC8 WAS 500 FT BELOW US AND APPROX 1/4 MI TO OUR R. AFTER MAKING A L TURN AND GETTING BACK OVER TO RWY 21L THE CTLR SAID WE WERE 3 1/2 MI IN TRAIL OF THE A320 AND 30 KTS FASTER. WE SLOWED TO OUR FINAL APCH SPD AND EVENTUALLY MADE A GAR BECAUSE THE A320 DID NOT CLR THE RWY. THE FIRST TIME WE HAD HEARD RWY 21L WAS AFTER THE CTLR GAVE US THE IMMEDIATE L TURN TO 180 DEGS AND THEN SAID TO FOLLOW THE A320 TO RWY 21L. DETROIT NORMALLY HANDLES MUCH MORE TFC AND THE LIGHT TFC AT THE TIME OF OUR ARR MAY HAVE CAUSED THE CTLR TO RELAX AND NOT SPECIFY THE RWY HE EXPECTED US TO USE WHEN HE SAID 'FOLLOW THE A320 TO THE ARPT.' SUPPLEMENTAL INFO FROM ACN 324268: WHEN APCHING ARPT 10 MI OUT WE WERE ASKED TO FOLLOW A320 VISUALLY (NO RWY MENTIONED). WE WERE ALSO INFORMED OF A DC8 BY APCH CTL. THE DC8 APPEARED TO BE CLOSE TO OUR ACFT SO I ASKED CAPT AND FO TO CONFIRM OUR LNDG RWY. WE THEN RECEIVED A TCASII RA TO CLB AND WE DID. DC8 WENT BENEATH US. THEN APCH CTL TOLD US TURN L AND THEN CLRED US FOR RWY 21L APCH. (RWY 21R APCH FREQS AND COURSES WERE ALREADY SET AND WE SUBSEQUENTLY CHANGED THEM TO RWY 21L APCH FREQS AND COURSES.) SUPPLEMENTAL INFO FROM ACN 323766: WHEN APCHING THE ARPT ABOUT 10 MI OUT; WE WERE ASKED TO FOLLOW AN A320; WHICH WAS INSIDE US ON A L BASE; VISUALLY (NO RWY WAS MENTIONED). THE A320 OVERSHOT RWY 21L AND RWY 21C AND APPEARED TO BE HDG TO RWY 21R ALSO. WE WERE ALSO INFORMED BY APCH OF A DC8 THAT WAS 2 MI AWAY. I (CAPT) DID NOT SEE THE DC8 AND WAS CONCENTRATING ON KEEPING SPACING ON THE A320; BUT THE DC8 WAS SEEN BY BOTH THE FO AND SO. ABOUT 3000-4000 FT WE RECEIVED A CLB TCASII RA; WHICH I FOLLOWED. WE CONTACTED DTW TWR; SLOWED TO APCH SPD AS WE WERE STILL CLOSE TO THE A320. ULTIMATELY WE HAD TO MAKE A GAR BECAUSE THE A320 DID NOT CLR RWY 21L IN TIME. AFTER THE GAR WE MADE AN UNEVENTFUL LNDG ON RWY 21L.