The code consists of four digits. For the code to be valid, the first two digits must be even and the last two digits must be odd. What is the probability that a randomly chosen valid code has at least one pair of adjacent digits that are the same?
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.
The code consists of four digits. For the code to be valid, the first two digits must be even and the last two digits must be odd. What is the probability that a randomly chosen valid code has at least one pair of adjacent digits that are the same?
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