Use the counting unions method, counting cartesian product or pigeon principle method to get the answerExpress your response via sets you dene before computing a value below. For example, you might begin your response with `A = set of some objects`, `B = set of some other objects` and then compute some expression for what you're seeking to count: (see image)1 in the image means Henry requires only that he have one shoe for his right foot and another shoe for his left foot, they needn't match Certainly! Here's the transcription and explanation:---**Combination Problems****Problem i**Regular MA license plates have 3 digits followed by 3 (uppercase) letters, e.g., ‘924 VXA’ or 4 digits followed by 2 (uppercase) letters, e.g., ‘2012 CS’. How many different license plates are possible?**Problem ii**Henry owns 3 hiking shoes and 5 running shoes for his left foot. He owns 12 running shoes for his right foot. How many different pairs of shoes, one left and one right, can he form?**Note**: The formula displayed above the problems illustrates how to calculate the number of combinations possible when multiplying different sets: \[ |A \times B| = |A| \times |B| = 3 \times 7 = 21 \] This means if set A has 3 elements and set B has 7 elements, then the combination of the two sets $ A \times B $ will have 21 elements.--- This explanation provides a foundation for understanding how to approach these types of problems using combinations and permutations.

Concept Used: If set A has n element i.e. for Position A we have n number of choices and set B has…

Answered: |A x B| = |A| x |B| = 3 * 7 = 21 i…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use the counting unions method, counting cartesian product or pigeon principle method to get the answer

Express your response via sets you dene before computing a value below. For example, you might begin your response with `A = set of some objects`, `B = set of some other objects` and then compute some expression for what you're seeking to count: (see image)

¹in the image means Henry requires only that he have one shoe for his right foot and another shoe for his left foot, they needn't match

Certainly! Here's the transcription and explanation:

---

**Combination Problems**

**Problem i**

Regular MA license plates have 3 digits followed by 3 (uppercase) letters, e.g., ‘924 VXA’ or 4 digits followed by 2 (uppercase) letters, e.g., ‘2012 CS’. How many different license plates are possible?

**Problem ii**

Henry owns 3 hiking shoes and 5 running shoes for his left foot. He owns 12 running shoes for his right foot. How many different pairs of shoes, one left and one right, can he form?

**Note**: The formula displayed above the problems illustrates how to calculate the number of combinations possible when multiplying different sets:
\[ |A \times B| = |A| \times |B| = 3 \times 7 = 21 \]

This means if set A has 3 elements and set B has 7 elements, then the combination of the two sets $ A \times B $ will have 21 elements.

---

This explanation provides a foundation for understanding how to approach these types of problems using combinations and permutations.

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