Select uniformly at random a permutation of {1, 2, ..., 100}. What is the probability that in the selected permutation all numbers are in ascending order? I understand there is a total of 100! permutations, but I have no idea how many permutations are in ascending order.
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.
Select uniformly at random a permutation of {1, 2, ..., 100}. What is the probability that in the selected permutation all numbers are in ascending order?
I understand there is a total of 100! permutations, but I have no idea how many permutations are in ascending order.
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