2024 ASRJC P2 Q8

An office team of \(10\) people includes \(7\) men and \(3\) women named Anne, Beth, and Cathie. For an upcoming fire drill exercise, \(5\) individuals will be chosen, each assigned a unique role, to carry out the drill. Determine the number of possible ways to select \(5\) people from this group of \(10\)

1. to conduct the fire drill,[1]
2. such that at most \(1\) woman is selected to conduct the fire drill.[2]
3. After the fire drill exercise, the \(10\) people are to hold a discussion at a round table with \(10\) identical seats. Determine the number of ways in which Beth is seated between Anne and Cathie.[1]
4. A group photo of the \(10\) people, arranged in two rows of five, was taken after the discussion. Determine the number of ways in which Beth is not standing beside Anne or Cathie.[4]