The Jacksons are planning their next family night. They always have dinner out somewhere and then do something fun together. There are 2 adults and 2 children in the family. Each family member is allowed 2 meal suggestions, and each child is allowed 2 activity suggestions. Assuming no family members choose the same thing, how many different family night possibilities are there?
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.
The Jacksons are planning their next family night. They always have dinner out somewhere and then do something fun together. There are 2 adults and 2 children in the family. Each family member is allowed 2 meal suggestions, and each child is allowed 2 activity suggestions. Assuming no family members choose the same thing, how many different family night possibilities are there?
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