John is one of twelve members of the Math Honor Society at his school. A delegation of four members must be chosen to represent the school in the Math Competition. How many different delegations could be chosen that include John? How many different delegations could be chosen that do not include John?
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.
John is one of twelve members of the Math Honor Society at his school. A delegation of four members must be chosen to represent the school in the Math Competition.
How many different delegations could be chosen that include John?
How many different delegations could be chosen that do not include John?
There are ____combinations including John and ___ different combinations excluding John.
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