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The problem in the image involves arranging cards numbered 1 to 9 under specific conditions. Here’s the breakdown of the two sub-parts of the problem:

### Problem Description
- **Cards** numbered from **1 to 9** are to be arranged in a row.
- **Odd-numbered cards** must be arranged in **increasing order** from left to right. 
- **Even-numbered cards** can be placed in **any order**.

#### Part (a)
You are asked:
- **How many ways** can this be done for all nine cards?

#### Part (b)
You are asked:
- **How many ways** can eight of these cards be selected and arranged in a row, such that the odd-number

Consider a collection of cards numbered from 1 to 9. All nine cards are arranged in a row so that the odd numbers are in increasing order, while the even numbers can be in any order. (a) How many ways can this be done? (b) How many ways can eight of these cards be selected and then arranged in a row so that the odd numbers are in increasing order?

Learn how to solve a combinatorics problem involving the arrangement of cards numbered 1 to 9. The odd-numbered cards must be arranged in increasing order, while the even-numbered cards can be in any order. Find out how many ways this can be done for both nine cards and a selected set of eight cards. Suitable for students in Grades 9-12.

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