Out of the 12 people applying for a scholarship, a) how many ways can we select a group of five to interview? b) Out of the five finalists, how many ways could we select three and also rank them first, second, and third?
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.
Out of the 12 people applying for a scholarship,
a) how many ways can we select a group of five to interview?
b) Out of the five finalists, how many ways could we select three and also rank them first, second, and third?
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