Ben and Charles were in their police cruiser making their way down Main Street. They$$d just come from investigating a break$-$in at Eagle Chevrolet and were hungry for some Wendy$$s$.$ Charles was partial to the spicy chicken sandwich. Ben just couldn$$t go another minute without a triple with bacon. But lunch was not to be$.$ They$$d gotten about a block past Citizen$$s Bank when the alarm sounded and the officers looked back to see Derrick and Freida sprinting in the opposite direction. Ben was driving and slammed on the brakes to make a u$-$turn but when he did, Gretchen rear ended the cruiser. She put her car in park and got out to check the damage and in so doing, blocked Ben from being able to complete his turn to go after the fleeing pair. Undeterred, Charles jumped out of the cruiser and took off in the direction Derrick and Freida were running in$.$

Derrick and Freida had crossed Main Street and were making their way down second street, not knowing Charles was gaining on them from behind. With a$,$See ya$,$ Derrick,$$ Freida took a turn and headed up past ADUC toward her dorm. It was decision time for Charles, who decided to try to catch up with Derrick. Without slowing down in the least, Derrick sprinted straight across Elizabeth Avenue and into his house and had just plopped down on the sofa when Charles came through his front door and shouted, $$Put your hands where I can see them! You$$re under arrest!$$ He had Derrick stand to the side while he searched the coffee table drawers and sofa cushions. In the sofa cushions he found a roach $($which for those of you who don$$t know, is the burnt stub end of a joint $($which for those of you who don$$t know is a marijuana cigarette$)).$

Question: Assuming Officer Charles had probable cause to believe Derrick had committed a robbery, was his warrantless entry into Derrick's house lawful?