SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Understanding the Generalized Multiplication Principle through Exercises

aladdin-francis avatar
aladdin-francis
10 diapositives · 260 Views · Nov 29, 2014

This section explores the Generalized Multiplication Principle, which states that if a task involves consecutive operations, the total number of ways to perform the task can be found by multiplying the number of options for each operation. Through numerous exercises involving word formation, glove selection, and coin tosses, we delve into identifying tasks and operations, while applying restrictions when necessary. These applications enhance our understanding of combinatorial counting methods, providing a solid foundation in probability and discrete mathematics.

Understanding the Generalized Multiplication Principle through Exercises - slide 1
01 / 10Understanding the Generalized Multiplication Principle through Exercises
1 / 17

Télécharger la présentation

Understanding the Generalized Multiplication Principle through Exercises
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Chapter 5 Section 4 The Multiplication Principle

  2. Generalized Multiplication Principle • If a task consists of toperations performed consecutively, then the task can be performed in m1• m2• m3• m4• … • mt ways. • Trick is to identify the task and the operations.

  3. Exercise 3 (page 228) • How many two-letter words (including non-sense words) can be formed? Note: • Task: Form two-letter word • Two operations • Write the first letter • Write the second letter • Restriction(s): None Solution: 26• 26 = 676

  4. Exercise 7 (page 228) • Have 5 different pairs of gloves • How many ways can you select a right-handed glove and a left-handed glove such that they don’t match? Note: • Task: Select two gloves • Two operations • Pick the right-handed glove • Pick the left-handed glove • The authors assume that you pick the right-handed glove first. • Restriction(s): The two gloves can not match

  5. Exercise 7 Solution __ • __ = # of ways For selecting the right-handed glove: 5• _ For selecting the left-handed glove: 5• 4 Answer: 5• 4 = 20

  6. Exercise 11 (page 228) • Toss a coin 6 times and observe the sequence of heads and tails. How many different sequences? Note: • Task: Observe the sequence of heads and tails • Six operations • First coin toss • Second coin toss (etc.) 6. Sixth coin toss • Restriction(s): None

  7. Exercise 11 Solution Task: __ • __ • __• __• __ • __ Answer: 2• 2• 2• 2• 2• 2 = 26 = 64

  8. Exercise 23 Part (b) (page 229) • Set: { h , o , t , s , m , x , e } • How many four letter words (including nonsense words) can be formed with the restriction: Letters cannot repeat. Solution: 7• 6• 5• 4 = 840

  9. Exercise 23 Part (c) (page 229) • Set: { h , o , t , s , m , x , e } • How many four letter words (including nonsense words) can be formed with the restriction: Begins with ‘h’ and repetitions are allowed. Solution: 1• 7• 7• 7 = 343

  10. Exercise 23 Part (d) (page 229) • Set: { h , o , t , s , m , x , e } • How many four letter words (including nonsense words) can be formed with the restrictions: Word must end in vowel and repetitions are not allowed. Solution: 6• 5• 4• 2 = 240