8) Suppose that in a lottery game you are to pick five different integers between 1 and 50, including 1 and 50, where the order of the numbers doesn't matter and you choose the numbers at the same time, and a sixth integer between 1 and 40, including 1 and 40. (The sixth number could potentially be the same as one of the first 5 numbers.) a) What is the probability that you get a prize for matching the first five numbers but not the sixth number? b) What is the probability that you get a prize for matching at least 3 of the first five numbers and matching the sixth number?
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.
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