AMC 10 Weekly Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 15 Medium

Assign 6 doctors to units A, B, and C for nucleic acid testing, with 2 doctors assigned to each unit. Doctor a cannot go to unit A, and doctor b can only go to unit B. How many different assignment methods are there?

  • A.

    18

  • B.

    24

  • C.

    30

  • D.

    36

  • E.

    42

Answer:A

According to the problem, we discuss two cases:

 

① If a goes to unit B, then a and b are together in unit B. The remaining 4 people are divided into 2 groups and assigned to units A and C. The number of arrangements is

\tfrac{1}{2}\,_{4}C_{2}\times\,_{2}P_{2}=6.

 

② If a does not go to unit B, then a must go to unit C. From the remaining 4 people, choose 2 to be assigned to unit A, and then assign the remaining 2 people to units B and C. The number of arrangements is

\,_{4}C_{2}\times\,_{2}P_{2}=12.

 

Therefore, the total number of arrangements is

6+12=18.

 

Thus, the answer is A.

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