Question

n the game of Clue, there are 6 suspects, 9 rooms and 6 weapons. How many different combinations of suspects, locations and weapons are there

Answers

    • (A) The number of solutions possible is 324.
    • (B) x in terms of s, w, and r is given by x = (6 – s)(6 – w)(9 – r).
    (A) To find how many solutions are possible:
    Given that the game of clues involves 6 suspects, 6 weapons, and 9 rooms.
    The number of ways that one of each is randomly chosen is given by:
    • ⁶C₁ × ⁶C₁ × ⁹C₁ = 6 × 6 × 9 = 324
    Therefore, the number of solutions possible is 324.
    (B) To express x in terms of s, w, and r:
    • Given that a player is randomly given three of the remaining cards, let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player.
    • The number of suspects, weapons, and rooms remaining respectively after the player observes his or her three cards are,
           6 – s, 6 – w, and 9 – r.
    Let x denote the number of solutions that are possible after that player observes his or her three cards, then:
    • x = 6-s∧C₁ × 6-w∧C₁  × 9-r∧C₁ = (s-6)(6-w)(9-r)
    Therefore, x in terms of s, w, and r is given by x = (6 – s)(6 – w)(9 – r).
    So, answers to both the subparts are shown.
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    The correct question is given below:
    The game of clues involves 6 suspects, 6 weapons, and 9 rooms. one of each is randomly chosen and the object of the game is to guess the chosen three. (A) How many solutions are possible? in one version of the game, the selection is made and then each of the players is randomly given three of the remaining cards. let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player. also, let x denote the number of solutions that are possible after that player observes his or her three cards.(b) express x in terms of s, w, and r.

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