2018 AMC 10B Problems/Problem 3
Contents
[hide]Problem
In the expression each blank is to be filled in with one of the digits or with each digit being used once. How many different values can be obtained?
Solution 1 - Combinations
We have ways to choose the pairs, and we have ways for the values to be switched so
Solution 2
We have four available numbers . Because different permutations do not matter because they are all addition and multiplication, if we put on the first space, it is obvious there are possible outcomes .
Solution 3
There are exactly ways to arrange the numbers and overcounts per way due to commutativity. Therefore, the answer is
~MC_ADe
Video Solution (HOW TO THINK CRITICALLY!!!)
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
2018 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.