# Difference between revisions of "2015 AMC 8 Problems/Problem 10"

(Created page with "How many integers between <math>1000</math> and <math>9999</math> have four distinct digits? <math>\textbf{(A) }3024\qquad\textbf{(B) }4536\qquad\textbf{(C) }5040\qquad\textb...") |
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<math>\textbf{(A) }3024\qquad\textbf{(B) }4536\qquad\textbf{(C) }5040\qquad\textbf{(D) }6480\qquad \textbf{(E) }6561</math> | <math>\textbf{(A) }3024\qquad\textbf{(B) }4536\qquad\textbf{(C) }5040\qquad\textbf{(D) }6480\qquad \textbf{(E) }6561</math> | ||

+ | ==Solution 1== | ||

+ | The question can be rephrased to "How many four-digit positive integers have four distinct digits," since numbers between <math>1000</math> and <math>9999</math> are four-digit integers. There are <math>9</math> choices for the first number, since it cannot be <math>0</math>, <math>9</math> choices 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> numbers between <math>1000</math> and <math>9999</math> with four distinct digits. |

## Revision as of 16:58, 25 November 2015

How many integers between and have four distinct digits?

## Solution 1

The question can be rephrased to "How many four-digit positive integers have four distinct digits," since numbers between and are four-digit integers. There are choices for the first number, since it cannot be , choices 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 numbers between and with four distinct digits.