A census taker visited the Jones household, and asked Mrs. Jones for the age of her three sons. Mrs. Jones, a math professor, answered, “See if you can work this out. If you multiply the three ages together, you get a total of seventy-six. If you add the three ages together, you get a total that is the same number on the front door of my house.” The census taker looked at the number on the front door of the house and scribbled a few computations on a piece of paper. A few minutes later, the census taker replied to Mrs. Jones, “You did not give me enough information to determine the ages of your three sons.” “Good job that you found that out,” answered Mrs. Jones, “I forgot to tell you that my oldest son has a pet dog with three legs, named Tripod.” “Thank you. Now I know,” concluded the census taker. What are the three ages of Mrs. Jones three sons?
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.
A census taker visited the Jones household, and asked Mrs. Jones for the age of her three sons. Mrs. Jones, a math professor, answered, “See if you can work this out. If you multiply the three ages together, you get a total of seventy-six. If you add the three ages together, you get a total that is the same number on the front door of my house.” The census taker looked at the number on the front door of the house and scribbled a few computations on a piece of paper. A few minutes later, the census taker replied to Mrs. Jones, “You did not give me enough information to determine the ages of your three sons.” “Good job that you found that out,” answered Mrs. Jones, “I forgot to tell you that my oldest son has a pet dog with three legs, named Tripod.” “Thank you. Now I know,” concluded the census taker. What are the three ages of Mrs. Jones three sons?
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