Difference between revisions of "2015 AMC 8 Problems/Problem 10"
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There are <math>9</math> choices for the first number, since it cannot be <math>0</math>, there are only <math>9</math> choices left for the second number since it must differ from the first, <math>8</math> choices for the third number, since it must differ from the first two, and <math>7</math> choices for the fourth number, since it must differ from all three. This means there are <math>9 \times 9 \times 8 \times 7=\boxed{\textbf{(B) }4536}</math> integers between <math>1000</math> and <math>9999</math> with four distinct digits. | There are <math>9</math> choices for the first number, since it cannot be <math>0</math>, there are only <math>9</math> choices left for the second number since it must differ from the first, <math>8</math> choices for the third number, since it must differ from the first two, and <math>7</math> choices for the fourth number, since it must differ from all three. This means there are <math>9 \times 9 \times 8 \times 7=\boxed{\textbf{(B) }4536}</math> integers between <math>1000</math> and <math>9999</math> with four distinct digits. | ||
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+ | If you're too lazy to do <math>9 \times 9 \times 8 \times 7= 4536</math>, we can notice <math> 9 \times 9 = 81</math> and <math> 8 \times 7=56</math> The unit digit must be 6. Therefore the answer is the only answer with a a unit digit of 6. <math>\boxed{B}</math>) | ||
==Video Solution (HOW TO THINK CRITICALLY!!!)== | ==Video Solution (HOW TO THINK CRITICALLY!!!)== |
Latest revision as of 10:10, 18 August 2024
Contents
Problem
How many integers between and
have four distinct digits?
Solution 1
There are choices for the first number, since it cannot be
, there are only
choices left for the second number since it must differ from the first,
choices for the third number, since it must differ from the first two, and
choices for the fourth number, since it must differ from all three. This means there are
integers between
and
with four distinct digits.
If you're too lazy to do , we can notice
and
The unit digit must be 6. Therefore the answer is the only answer with a a unit digit of 6.
)
Video Solution (HOW TO THINK CRITICALLY!!!)
~Education, the Study of Everything
Video solution
https://youtu.be/Zhsb5lv6jCI?t=272
https://www.youtube.com/watch?v=OESYIYjZFdk ~David
~savannahsolver
See Also
2015 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.