AMC 10 Daily Practice - Counting

Complete problem set with solutions and individual problem pages

Problem 2 Easy

Using numbers 1, 2, 3, 4, 5 and, 6 to form a 6 digit number without repeating digits. 1 and 2 must be adjacent, and 3 and 4 must be non-adjacent. In how many ways can this happen?

  • A.

    72

  • B.

    144

  • C.

    216

  • D.

    288

  • E.

    312

Answer:B

Binding 1 and 2: _2P_2 ways to arrange them.

Arrange 1,2, 5, and 6: _3P_3 ways to arrange them.

Use star and bar method to place 3 and 4: {_4P_2} ways to fill in 3 and 4.

In total, there are _2P_2 \times _3P_3 \times _4P_2 = 144 ways.

Related Problems
Problem 1 AMC 10 Daily Practice - Counting
Problem 3 AMC 10 Daily Practice - Counting
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