Lesson Plans SET A for Grades 9-10-Lesson 7 Level 9-10 Combinatorics Homework Solutions

Lesson 7 Level 9-10 Combinatorics Homework Solutions

Pdf Summary

The document provides solutions to a set of combinatorics problems typically covered in a Level 9-10 curriculum. Below is a summary of the solutions presented:<br /><br />1. **Problem 1:** The task is to calculate the total number of permutations of the numbers 1, 5, 5, 7, 7, 9 and alternatively 3, 3, 5, 5, 7, 7. The solution uses factorial calculations considering the repeated digits and finds that there are a total of 45 distinct permutations.<br /><br />2. **Problem 2:** <br />   - **(a)** Six people can be seated in a row in 720 different ways, calculated using 6!.<br />   - **(b)** When wives must sit next to their husbands, treat the wives as a single unit, resulting in 144 different seating arrangements.<br />   - **(c)** Considering each couple can swap seats, results in 24 different seating arrangements.<br /><br />3. **Problem 3:** <br />   - **(a)** To form two groups of five from 15 people, the number of ways is calculated using combinations, leading to a result involving factorials divided by (5!)^3.<br />   - **(b)** In scenarios involving experienced hikers A and B, calculate the number of ways to assign the remaining 13 hikers to two distinct groups based on whether group sizes are 7 or 8.<br /><br />4. **Problem 4:** Combinatorial arrangements of codes with combinations of digits and letters are considered:<br />   - Calculate total possible codes using digits and letters, considering two cases of code arrangements (letters adjacent vs. letters non-adjacent).<br />   - Determine the probability of specific configurations where no two letters or digits are next to each other.<br /><br />5. **Problem 5:** <br />   - There are 495 ways to select a group of four students from twelve.<br />   - For the probability that each student comes from a different time zone, calculate the result as 9 out of 55.<br /><br />Overall, the solutions demonstrate the application of permutation and combination principles in solving complex arrangement and grouping problems.

Keywords

combinatorics

permutations

factorials

combinations

seating arrangements

probability

grouping problems

Level 9-10 curriculum

hikers

codes