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

Lesson 7 Level 9-10 Combinatorics Homework

Pdf Summary

The document consists of a set of combinatorics problems aimed at Level 9-10 students, as part of the Math Kangaroo class curriculum. The problems focus on applying combinatorial principles and encourage students to review their notes and materials for better understanding. <br /><br />1. **Problem 1** challenges students to find how many 6-digit numbers yield a product of 11025 from their digits. The answer provided is 45.<br /><br />2. **Problem 2** involves three couples attending a movie theater and addressing different seating arrangements. It comprises three parts:<br />   - (a) Calculating the total number of seating arrangements for all six individuals with numbered tickets from 30 to 35. The answer is 720.<br />   - (b) Determining seating arrangements where the wives must sit together. The result is 144 ways.<br />   - (c) Calculating seating arrangements where each couple must sit together, resulting in 24 ways.<br /><br />3. **Problem 3** engages students in grouping scenarios:<br />   - (a) The problem describes dividing 15 friends into 3 equal groups of 5 people, with the formula \( \frac{15!}{(5!)^3} \) provided for calculation.<br />   - (b) A second scenario involves dividing 15 people into two groups of 7 and 8, each led by one of the two experienced hikers. The answer is \( 2 \cdot \frac{13!}{7!6!} \).<br /><br />4. **Problem 4** concerns the probability of arranging a 5-character code with 3 digits and 2 letters so that no two digits or letters are adjacent. The probability is given as \( \frac{1}{10} \).<br /><br />5. **Problem 5** calculates the probability of selecting 4 students out of 12 such that each belongs to a different time zone. The answer is \( \frac{9}{55} \).<br /><br />These problems and solutions are designed to consolidate students' understanding of topics in combinatorics, offering them practice opportunities that deepen their conceptual grasp.

Keywords

combinatorics

Level 9-10

Math Kangaroo

6-digit numbers

seating arrangements

grouping scenarios

probability

combinatorial principles

student practice

conceptual understanding