AMC 8 Daily Practice Round 9

Complete problem set with solutions and individual problem pages

Problem 9 Easy

The school's basketball team currently has 5 boys and 6 girls. The coach wants to randomly select 3 people from the group to participate in the schools' 3v3 basketball league. How many ways can the 3 selected students be arranged such that at least one girl is included?

  • A.

    45

  • B.

    105

  • C.

    145

  • D.

    155

  • E.

    159

Answer:D

Number of choices of choosing 3 students from 11 students is:

P_1=\frac{11\times10\times9}{3\times2\times1}

Number of choices of choosing 3 students from 5 boys is:

P_2=\frac{5\times4\times3}{3\times2\times1}

P=P_1-P_2=\frac{11\times10\times9}{3\times2\times1}-\frac{5\times4\times3}{3\times2\times1}=155.

The answer is \text{D}.

Related Problems
Problem 7 AMC 8 Daily Practice Round 9
Problem 8 AMC 8 Daily Practice Round 9
Problem 10 AMC 8 Daily Practice Round 9
Problem 11 AMC 8 Daily Practice Round 9
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