AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 23 Medium

From 3 ones, 2 twos, and 1 three, if 3 digits are selected, how many different three-digit numbers can be formed?

  • A.

    15

  • B.

    16

  • C.

    17

  • D.

    18

  • E.

    19

Answer:E

Case 1:

3 digits all the same: 111, only 1.

Case 2:

2 of three digits are the same:

322, 232, 223, 311, 131, 113, 122, 212, 221, 211, 121, 112. There are 3+3+6=12 numbers.

Case 3:

All three digits are different: there are _{3}P_{3}=3\times 2\times 1=6 numbers.

Totally, 1+12+6=19 numbers.

Related Problems
Problem 21 AMC 8 Daily Practice Round 1
Problem 22 AMC 8 Daily Practice Round 1
Problem 24 AMC 8 Daily Practice Round 1
Problem 25 AMC 8 Daily Practice Round 1
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