Permutations with repetition - practice problems

Permutations with repetition count arrangements where some objects are identical, reducing the total number of distinct permutations. When arranging n objects where n₁ are of one type, n₂ of another, and so on, the formula is n!/(n₁!n₂!...nₖ!). For example, the word "MISSISSIPPI" has 11 letters with repetitions, giving 11!/(4!4!2!) distinct arrangements. This differs from standard permutations where all objects are unique. When unlimited repetition is allowed (like selecting with replacement), k items chosen from n options give n^k permutations. Applications include counting distinct arrangements of letters in words, distributing identical objects, and analyzing sequences with repeated elements. Understanding this concept is essential for advanced combinatorics and probability calculations.

Directions: Solve each problem carefully. Show all your work.

Number of problems found: 47

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