AMC 10 Weekly Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 13 Medium

Four volunteers A, B, C, and D are assigned to three soccer fields for volunteer service. Each volunteer must be assigned, and each soccer field must have at least one volunteer. However, A and B cannot be assigned to the same soccer field. How many different assignment plans are there?

  • A.

    24

  • B.

    28

  • C.

    30

  • D.

    36

  • E.

    42

Answer:C

Since A and B cannot be assigned to the same soccer field, there are two possible cases:

When A and B each serve on different soccer fields, there are _{3}P_{3} = 6 assignment plans.

When either A or B is assigned together with one of C or D to the same soccer field, there are _{2}C_{1} \times _{2}C_{1} \times _{3}P_{3} = 24 assignment plans.

Therefore, the total number of different assignment plans is 6 + 24 = 30.

Thus, the answer is C.

Related Problems
Problem 11 AMC 10 Weekly Practice Round 3
Problem 12 AMC 10 Weekly Practice Round 3
Problem 14 AMC 10 Weekly Practice Round 3
Problem 15 AMC 10 Weekly Practice Round 3
Think Academy Powered by ChatGPT