## Tanya Prepared 4 Different Letters To Be Sent To 4

A derangement is a type of permutation where none of the elements are in their original position. This results in no fixed points and can be represented by n! (n factorial). Derangements can also be viewed as disturbances of normal order or disruptions in the language of permutations. James Grime has further explored the concept of derangements. Synonyms of derangements include "disruptions" or "an act of changing the order of things." Derangements can be seen in various contexts, such as in math or the human mind. There are multiple examples and definitions of derangements available.

To solve the problem, we can use the concept of derangements. In combinatorial mathematics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. The number of derangements of a set of n elements is given by the formula "n! * (1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!)." For the given problem, there are 4 letters and 4 envelopes. The number of derangements when n = 4 is 9. Therefore, the probability that only 1 letter will be put into the envelope with its correct address is 9/24, which simplifies to 3/8.

So, the probability that only 1 letter will be put into the envelope with its correct address is 3/8.

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