In how many ways can one person, one weapon, and one room be chosen?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
In the board game CLUE, there are 6 people (Mrs. White, Miss Scarlet, Mrs. Peacock, Mr. Green, Professor Plum, and Colonel Mustard), there are 6 weapons (knife, wrench, candlestick, rope, lead pipe, and revolver) and there are 9 rooms (ballroom, billiard room, conservatory, dining room, hall, kitchen, library, lounge, and study). Each time you play the game a person, a weapon, and a room are secretly chosen. In order to win the game you must figure out who did the crime, what they did the crime with, and where they committed the crime.
- In how many ways can one person, one weapon, and one room be chosen?
- If you have no clue about the three secretly chosen cards, what is the
probability of guessing the solution?
- If you know that the rope was used to commit the crime, what is the probability of guessing the solution?
1.
Total ways = 6*6*9 = 324
6 ways for person, 6 ways for weapon, and 9 ways to select one room
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