AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 10 Medium

Class 3 of Grade 4 is holding a Children’s Day celebration. The entire program consists of 2 dances, 2 songs, and 3 skits. If programs of the same type must be performed consecutively, then there are            different possible performance orders.

  • A.

    122

  • B.

    144

  • C.

    155

  • D.

    166

  • E.

    177

Answer:B

Since programs of the same type must be performed consecutively, we can apply the “bundling method.” First, arrange the three types of programs (dance, song, skit). Then, within each type, arrange the specific programs.

Therefore, the total number of performance orders is _{3}P_{3} \times _{2}P_{2} \times _{2}P_{2} \times _{3}P_{3} = 144 \quad (\text{orders}).

Related Problems
Problem 8 AMC 8 Daily Practice Round 1
Problem 9 AMC 8 Daily Practice Round 1
Problem 11 AMC 8 Daily Practice Round 1
Problem 12 AMC 8 Daily Practice Round 1
Think Academy Powered by ChatGPT