Alice and Bob are talking over a really slow telephone connection and want to avoid talking over each other. They adopt the following scheme. Each person makes 8 cards numbered 0, 1, 2, 3, 4, 5, 6, 7, shuffles them and picks one at random. If the card says x, then the person waits x seconds before speaking. What is the probability that Alice and Bob will still start talking at the same time after this process?
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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