In a certain company, there are seven executives: Adam, Ben, Chris, David, Emily, Fiona, and Grace. They are seated in a row of chairs. The following conditions must be met:
i. Adam cannot sit next to Chris or Emily.
ii. Ben must sit next to David.
iii. Fiona cannot sit at either end of the row. Which of the following is a valid arrangement of the executives?
An office building has five floors, numbered one through five. Each floor has a different color carpet: red, blue, green, yellow, and white. The following conditions must be met:
i. The red carpet cannot be on the top floor.
ii. The blue carpet must be above the green carpet but below the yellow carpet.
iii. The white carpet must be on a higher floor than the green carpet but cannot be on the top floor. In which of the following arrangements is the sequence of floors correctly matched with the colors of their respective carpets?
Five friends – Alex, Brian, Chris, David, and Eric – are participating in a singing competition. They will perform one after the other. The following conditions must be met:
i. Alex cannot perform before David or Eric.
ii. Brian must perform before Chris.
iii. David cannot be the first or last to perform. In which of the following sequences can the friends perform according to the given conditions?
Five books – A, B, C, D, and E – are placed on a shelf. The following conditions must be met:
i. Book A cannot be placed next to book B.
ii. Book C must be placed between books B and D.
iii. Book E must be placed somewhere to the right of book A.
Which of the following represents a valid arrangement of the books on the shelf, from left to right?
In a chess tournament, there are six players: Alice, Bob, Carol, David, Emily, and Frank. Each player plays exactly once against each of the other players. The following conditions must be met:
i. Alice must play against Bob and Emily.
ii. Carol cannot play against David or Frank.
iii. Emily must play against Alice and David.
How many different matches can be played in total?