AOPS-CP Week 4: Chapter 3: Correcting for Overcounting
Lesson Review
1. Permutations with repeated elements:
https://www.mathwarehouse.com/probability/permutations-repeated-items.php
2. Counting pairs of items (understand why we need to divide by 2)
Formula to find the sum of n numbers (understand how we derived it step by step).
1+2+3+…+(n-1) + n = n (n+1) /2
3. Counting with symmetries
a) rotational symmetry (round table seats) = n!/n = (n-1)!
b) reflective symmetry (flipping over, key chain) = n!/2n = (n-1)!/2
Homework:
Page 52: 3.2.1, 3.2.2., 3.2.3, 3.2.5
Page 57: 3.3.1, 3.3.3, *3.3.5 (it’s a bonus, but not difficult. Just try!)
Page 61: 3.4.1, 3.4.3
Final Tips:
Please do not try to remember the formulas by heart, instead, try to understand them, and learn how to derive them.
We value procedures. Please show all your steps/procedures in math problem solving: both in classwork and homework. You will benefit from it in the long run.
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