This year, there are ten freshmen, seven sophomores, eight juniors, and eight seniors are eligible to be on a committee. In how many ways can a dance committee of 8 students be chosen? ways In how many ways can a dance committee be chosen if it is to consist of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors. ways In how many ways can a dance committee be chosen if it is to consist of 4 juniors and 4 senions. ways Determine the probability of selecting a committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors. Write your answer in decimal form, rounded to the nearest thousandth. Answer: Determine the probability of selecting a committee consisting of 4 juniors and 4 senions. Write your answer in decimal form, rounded to the nearest thousandth. Answer:

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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.