Final answer:
The likely cause of death for a patient who took a combination of benzodiazepine, alcohol, and a barbiturate is respiratory arrest, due to the compounded depressive effects on the central nervous system and respiratory function.
Step-by-step explanation:
A patient who consumes a benzodiazepine in combination with alcohol and a barbiturate is at high risk of respiratory arrest due to the additive central nervous system and respiratory depressant effects of these substances. Benzodiazepines and barbiturates both enhance the inhibitory effect of GABA on the central nervous system, slowing down brain activity, including that which controls respiration.
When combined with alcohol, which is itself a central nervous system depressant, the risk of overdose and death increases significantly. The patient in the question likely died from respiratory arrest, which is a common cause of death in overdoses involving combinations of central nervous system depressants.