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### Course: Math for fun and glory>Unit 3

Lesson 1: 2013 AMC 10 A

# 2013 AMC 10 A #24

Video by Art of Problem Solving.  Problem from the MAA American Mathematics Competitions. Created by Art of Problem Solving.

## Want to join the conversation?

• How do you know when to use ! ?
• Well when you are trying to calculate the amount of combinations of something. Let's say you have 1,2, and 3. You have 3 slots to place it in to make a 3 digit number. For the first slot we have 3 possible. For the second only 2 because we used 1 up, and then the last slot you only have one choice. The total amount of possibilities is 3 X 2 X 1 which is 3!. This is called combinatorics.
(1 vote)
• What if A is playing different people per round
eg.
Instead of A-M, A-M in one round
isn't A-M, A-O, or some other combo like that possible?
• When the instructor does the last step in each tree, he counts the different ways he can reorder the "word" made up by his made combinations: "xxyyzz" can be reordered 90 different ways (see to ). This accounts for all those other combos.
• how do you do roots
• it is the opposite of a square, normally people just use a calculator
• What does vactoreol mean! = - 0
• its factorial and it basically means that n! = n x (n-1) x (n-2) ... 1. All the way to one. For example 3! = 3 x 2 x 1
(1 vote)
• at , what method does he uses to find the combination?
• what did he mean at ?
• At that point, Person A still needs to play two games with Person O, so these must comprise the top "level" of the round (although it should be noted that the "level" does not matter, as the three games are simultaneous).
Both Persons B and C need to play one game each with Persons M and N. Since one person can not be in two games at the same time, the choices are B-M/C-N or B-N/C-M.
These two rounds (of three games each) do not have to occur last, which is why he uses 6! to find how many ways the six rounds can form the match. :)
• At how did he get what he did, i don't understand
• Why did he divide 720 by 2!2!2! at ? And why are factorials involved?