Apply the Fundamental Properties of Counting or Permutation to solve for the following problems. 1. A quiz bee competition consists of 12 contestants. The top 3 will receive scholarship for the next academic year. How many different permutations are there for the top 3 from the 12 contestants? 2. How many ways can a coach pick 5 plays from a set of 10 players? 3. How many different 5-card hands can be made from a standard deck of cards? 4. With repetitions allowed, how many words with or without meaning can be arranged from the word SWIM? 5. If three people are arranged in a five-seater bench and two people are arranged in a 6-seater bench, what are the total possible ways that both people are arranged?
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.
Apply the Fundamental Properties of Counting or Permutation to solve for the following problems.
1. A quiz bee competition consists of 12 contestants. The top 3 will receive scholarship for the next academic year. How many different permutations are there for the top 3 from the 12 contestants?
2. How many ways can a coach pick 5 plays from a set of 10 players?
3. How many different 5-card hands can be made from a standard deck of cards?
4. With repetitions allowed, how many words with or without meaning can be arranged from the word SWIM?
5. If three people are arranged in a five-seater bench and two people are arranged in a 6-seater bench, what are the total possible ways that both people are arranged?
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