Three fair coins are tossed. The two possible outcomes for a single coin are heads, h, and tails, t. Complete parts (a) through (e) below. (a) Write out the sample space. The sample space is . (Use commas to separate answers as needed.) (b) Determine the probability of no tails. The probability of no tails is. (Type an integer or a simplified fraction.) (c) Determine the probability of at least one tail. The probability of at least one tail is. (Type an integer or a simplified fraction.) (d) Determine the probability of no more than two tails. The probability of no more than two tails is (Type an integer or a simplified fraction.) (e) Determine the probability of exactly three tails. The probability of exactly three tails is. (Type an integer or a simplified fraction.)

Q: I need the answers for parts e to h please.

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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.