2015 AMC 8

Complete problem set with solutions and individual problem pages

Problem 10 Easy

How many integers between 1000 and 9999 have four distinct digits?

  • A.

    3024

  • B.

    4536

  • C.

    5040

  • D.

    6480

  • E.

    6561

Answer:B

There are 9 choices for the first number, since it cannot be 0, there are only 9 choices left for the second number since it must differ from the first, 8 choices for the third number, since it must differ from the first two, and 7 choices for the fourth number, since it must differ from all three. This means there are 9 \times 9 \times 8 \times 7=\boxed{\textbf{(B) }4536} integers between 1000 and 9999 with four distinct digits.

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