This topic contains 2 replies, has 2 voices, and was last updated by Neha 4 months ago.
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Viewing 3 posts - 1 through 3 (of 3 total)
Understanding Math Beyond the Classroom
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How it Works › Forums › Introductory Problems (AMC 8 Problems 10-20) › AMC 8 Review Session #1! (Geometry and Counting/Probability)
This topic contains 2 replies, has 2 voices, and was last updated by Neha 4 months ago.
Here are the introductory problems for the next $3$ days! These are more difficult than AMC 8 Problems 10-15 but they fit the range of $16-21$. Each of these problems are worth $5$ points to your leaderboard score! If you don’t understand one of the questions, feel free to post in the questions forum here
1. (Problem 5) In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is $X$, in centimeters?
2. (Problem 10) How many integers between $1000$ and $9999$ have four distinct digits?
3. (Problem 19) A triangle with vertices as $A=(1,3)$, $B=(5,1)$, and $C=(4,4)$ is plotted on a $6\times5$ grid. What fraction of the grid is covered by the triangle?
4. (Problem 11) In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel ($A, E, I, O,$ or $U$), the second and third must be two different letters among the $21$ non-vowels, and the fourth must be a digit ($0$ through $9$). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read “$AMC8$”?
Remember that you can post your solutions below to these problems and I will keep a running leaderboards for the top 10 students who participate the most! I especially appreciate the same problem being solved in different ways!
1) 7
2) 5040
4) 21000
For number 2, can we do complimentary counting with Principle of Inclusion-Exclusion?
I am really not sure how to do it though, there seems to be a lot of cases.