TRACON APCH CTLR APPARENTLY FORGOT WHICH RWY HE HAD ISSUED TO THE RPTR.

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WE WERE DSNDING ON APCH INTO THE DTW ARPT EARLY IN THE MORNING ON APR/WED/95. WE WERE ONE OF JUST A FEW AIRPLANES IN THE APCH CTLR'S AIRSPACE. WE HAD AN AIR TFC CTLR FROM THE MUSKEGON TWR ON OUR JUMP SEAT. ALL 3 OF US IN THE COCKPIT THOUGHT WE HAD HEARD FROM THE APCH CTLR TO EXPECT THE ILS TO RWY 21L. WE BRIEFED THE RWY 21L APCH AND PROCEEDED TO INTERCEPT THE RWY 21L LOC ON THE INTERCEPT HDG PROVIDED BY THE CTLR. JUST AS WE WERE INTERCEPTING THE LOC; HE GAVE US ANOTHER INTERCEPT HDG OF 240 DEGS. I TOLD HIM WE WERE COMING ONTO THE LOC. HE TOLD US WE WERE CLRED FOR THE RWY 21R APCH; NOT RWY 21L. AFTER A SHORT PAUSE HE CLRED US FOR THE RWY 21L APCH. WE WERE IN VMC CONDITIONS WITH A HIGH OVCST ABOVE US. THERE WASN'T MUCH TFC IN THE AIR AT THIS TIME. I THINK THERE WERE A FEW FACTORS THAT LED TO THIS. FIRST WAS THE TIME OF DAY. ALTHOUGH WE ALL HAD ADEQUATE REST PERIOD THE NIGHT BEFORE; THE XA00 AM WAKE-UP CALL FOR THE XB50 AM DEP DOESN'T PUT YOU IN THE CLEAREST OF MIND SITS AT THAT TIME OF DAY. ALSO; THE CTLR SEEMED TO BE IN A VERY BAD MOOD. AFTER INITIAL CALL-UP; I REMARKED 'SOMEONE GOT UP ON THE WRONG SIDE OF THE BED THIS MORNING OR ELSE HE'S AT THE END OF HIS SHIFT!' THE CTLR WAS REALLY SHORT WITH EVERYONE AND SOUNDED LIKE IT WAS A BIG EFFORT TO TALK ON THE RADIO. I BELIEVE OUR FRAME OF MINDS AND HIS FRAME OF MIND COMBINED TO CAUSE THIS CONFUSION. ONCE ON THE GND; THE CAPT SAID 'I NEVER HEARD HIM SAY RWY 21R.' I AGREED WITH HIM. THE CTLR ON THE JUMP SEAT EVEN SAID 'I HATE TO DISAGREE WITH ANOTHER CTLR; BUT I THOUGHT I HEARD HIM SAY RWY 21L ALSO.' THERE WAS NEVER A CONFLICT WITH ANY OTHER AIRPLANE IN THE AREA.