AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 22 Medium

Given the four digits 2, 0, 1, 7, each digit may be used at most once. How many natural numbers less than 2017 can be formed?

  • A.

    33

  • B.

    35

  • C.

    37

  • D.

    41

  • E.

    45

Answer:C

The natural numbers that satisfy the condition can be divided into 4 categories:

One-digit numbers: 0, 1, 2, 7, a total of 4.

Two-digit numbers: The first digit cannot be 0, and digits cannot be repeated, so there are 3 \times 3 = 9 numbers.

Three-digit numbers: The first digit cannot be 0, and digits cannot be repeated, so there are 3 \times 3 \times 2 = 18 numbers.

Four-digit numbers: The first digit cannot be 0, and digits cannot be repeated, so there are 3 \times 2 \times 1 = 6 numbers.

Therefore, in total, the number of natural numbers less than 2017 that can be formed is 4 + 9 + 18 + 6 = 37.

Related Problems
Problem 20 AMC 8 Daily Practice Round 1
Problem 21 AMC 8 Daily Practice Round 1
Problem 23 AMC 8 Daily Practice Round 1
Problem 24 AMC 8 Daily Practice Round 1
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