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3. First, write down 12 pairwise distinct permutations of the following 10 letters: a, a, a, b, b, n, n, e, s, t. Then prove that the number of pairwise distinct permutations of n objects in which the first object appears k₁ times, the second k₂ times, the third k3 times, and all other objects appear exactly once equals n! k₁! . k2!. k3!

3. First, write down 12 pairwise distinct permutations of the following 10 letters: a, a, a, b, b, n, n, e, s, t. Then prove that the number of pairwise distinct permutations of n objects in which the first object appears k₁ times, the second k₂ times, the third k3 times, and all other objects appear exactly once equals n! k₁! . k2!. k3!

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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3. First, write down 12 pairwise distinct permutations of the following 10 letters: a, a, a, b, b, n, n, e, s, t. Then prove that the number of pairwise distinct permutations of n objects in which the first object appears k₁ times, the second k₂ times, the third k3 times, and all other objects appear exactly once equals n! k₁! · k2! · k3!`
Transcribed Image Text:3. First, write down 12 pairwise distinct permutations of the following 10 letters: a, a, a, b, b, n, n, e, s, t. Then prove that the number of pairwise distinct permutations of n objects in which the first object appears k₁ times, the second k₂ times, the third k3 times, and all other objects appear exactly once equals n! k₁! · k2! · k3!`
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