AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 21 Medium

Using the digits 1, 2, 3, 4 to form three-digit numbers without repeating digits, if one such number is chosen at random, what is the probability that the selected number is a multiple of 3?

  • A.

    \frac{1}{4}

  • B.

    \frac{1}{3}

  • C.

    \frac{1}{2}

  • D.

    \frac{3}{4}

  • E.

    \frac{1}{3}

Answer:C

There are 4 possible combinations to form three-digit numbers. Among them, the combinations (1,2,3) and (2,3,4) produce multiples of 3, giving a total of 2 such combinations.

Therefore, the probability is \frac{2}{4} = \frac{1}{2}.

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