B757 FO MISSES DESCEND VIA CLEARANCE WHILE CAPT IS ON PA AND IS SUBSEQUENTLY UNABLE TO MAKE CROSSING RESTRICTION ON RIIVR1 INTO LAX.

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I; FO; WAS FLYING AND HANDLING RADIOS WHILE CAPT WAS SPEAKING TO THE PAX. I THOUGHT I HEARD AND REPEATED FROM ATC; 'CLEARED RIIVR ONE ARRIVAL FOR RWY 24R.' WE HAD ALREADY SET UP THE FMS FOR RIIVR ONE TO RWY 25L. WHEN THE CAPT WAS DONE SPEAKING WITH THE PAX; I REPEATED THE CLEARANCE AS NOTED ABOVE. HE WENT INTO THE FMS TO CHANGE THE ARRIVAL RWY TO RWY 24R. IT WAS NOT AN EASY CHANGE AND TOOK THE CAPTAIN MAYBE A MINUTE TO COMPLETE. HE THEN QUERIED ME AS TO SHOULD WE BE DESCENDING. I SAID I DIDN'T THINK SO BUT HE KNEW WE WERE WELL ABOVE OUR PROFILE. HE QUERIED ATC AND THEY SAID WE WERE CLEARED TO 'DESCEND VIA RIVVR ONE ARRIVAL.' SUBSEQUENTLY; WE WERE UNABLE TO MAKE THE ALTITUDE REQUIREMENT AT RIIVR BETWEEN 14000 FT AND 12000 FT. I BELIEVE ACTUAL ALTITUDE WAS 17000 FT. WHEN HE INITIALLY REALIZED WE WERE HIGH; HE NOTIFIED ATC. I DIDN'T HEAR 'DESCEND VIA' NOR DID ATC QUERY MY READBACK OF 'CLEARED VIA RIIVR ONE ARRIVAL TO RWY 24R.' THE CAPT WAS BUSY WITH THE FMS CHANGING RUNWAYS BEFORE HE REALIZED WE WERE HIGH. SOLUTION? MAYBE AN EASIER WAY TO SELECT DIFFERENT RUNWAYS ON THIS PARTICULAR ARRIVAL. ALSO; ATC TO MAKE SURE READBACK OF 'DESCEND VIA' FROM CREWS.