If life worked like the game show “Jeopardy,” the clue would be: “The amount Alex Trebek donated to a Pacoima nonprofit.” And the correct response would be: “What is $100,000?” Ken Craft, chief executive at Hope of the Valley Rescue Mission, first received a call from Trebek, the host of “Jeopardy” who is battling pancreatic cancer, in January. Later, Trebek visited the organization’s construction site for a homeless “navigation center” in North Hollywood. Later, Trebek invited Craft to his house for a talk – and the check. He also invited Craft and his wife, Laurie Craft, to a taping of “Jeopardy.” Hope of the Valley runs housing facilities, including three designed for homeless families, three cold-weather shelters and a substance abuse home. It operates thrift stores in Granada Hills, Simi Valley, Santa Clarita and Palmdale. In recognition of the donation, the Alex and Jean Trebek Multipurpose Room is scheduled to open in June at the NoHo center.