Select correct alternative from the given choices. Eight...

Select correct alternative from the given choices. Eight letters are to be placed in eight addressed envelopes. If the letters are placed at random into the envelopes, the probability that exactly one letter is placed in a wrong addressed envelopes is (A) $\frac{1}{6}$ (B) $\frac{1}{8 !}$ (C) $\frac{1}{7 !}$ (D) None of these

Select correct alternative from the given choices.
Eight letters are to be placed in eight addressed envelopes. If the letters are placed at random into the envelopes, the probability that exactly one letter is placed in a wrong addressed envelopes is
(A) $\frac{1}{6}$
(B) $\frac{1}{8 !}$
(C) $\frac{1}{7 !}$
(D) None of these

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Permutations

Permutations refer to the different ways of arranging a set of objects in order. They are fundamental in combinatorics and are used to model the number of possible outcomes in various scenarios where order matters, such as assigning letters to envelopes.

Fixed Points in Permutations

In the context of permutations, a fixed point occurs when an element appears in its designated position (for example, a letter correctly placed in the addressed envelope). Counting fixed points is crucial in problems where some objects must remain in their original positions.

Derangements

Derangements are a special type of permutation where none of the objects appear in their original positions. They are significant in combinatorial problems that involve completely misplacing items, and their calculation normally involves using the inclusion?exclusion principle.

Inclusion-Exclusion Principle

The inclusion-exclusion principle is a counting method used to compute the number of ways to arrange objects subject to multiple constraints by systematically adding and subtracting the counts of overlapping cases. This principle is essential in deriving formulas for the number of derangements and for permutations with a specific number of fixed points.

Transcript

Please give Ace some feedback