AMC 10 Weekly Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 17 Medium

Assign volunteers A, B, C to classrooms numbered 1,2,3 for cleaning, with exactly one volunteer in each classroom. What is the probability that A is not assigned to classroom 3?

  • A.

    \frac{2}{3}

  • B.

    \frac{3}{4}

  • C.

    \frac{1}{4}

  • D.

    \frac{1}{3}

  • E.

    \frac{3}{5}

Answer:A

Volunteers A, B, C are assigned to classrooms numbered 1,2,3,

with exactly one volunteer in each classroom. The possible assignments are:

(A,1),(B,2),(C,3),

(A,1),(B,3),(C,2),

(A,2),(B,1),(C,3),

(A,2),(B,3),(C,1),

(A,3),(B,1),(C,2),

(A,3),(B,2),(C,1),

a total of 6.

Among these, the cases where A is not assigned to classroom 3 are:

(A,1),(B,2),(C,3),

(A,1),(B,3),(C,2),

(A,2),(B,1),(C,3),

(A,2),(B,3),(C,1),

a total of 4.

Therefore, the probability that A is not assigned to classroom 3 is

P = \frac{4}{6} = \frac{2}{3}.

Thus, the answer is A.

Related Problems
Problem 15 AMC 10 Weekly Practice Round 3
Problem 16 AMC 10 Weekly Practice Round 3
Problem 18 AMC 10 Weekly Practice Round 3
Problem 19 AMC 10 Weekly Practice Round 3
Think Academy Powered by ChatGPT