AMC 10 Weekly Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 1 Easy

From 4 boys and 2 girls, select 3 people to form a team for the competition. If at least 1 girl must be included, then the total number of different ways to form the team is （   ）．

  • A.

    8

  • B.

    12

  • C.

    16

  • D.

    20

  • E.

    24

Answer:C

From the problem, the different selections can be divided into two cases:

 

Case 1: Exactly 1 girl is selected. The number of different ways is

_{2}C_{1}\times_{4}C_{2} = 12.

 

Case 2: Exactly 2 girls are selected. The number of different ways is

_{2}C_{2}\times_{4}C_{1}= 4.

 

According to the Addition Principle of Counting, the total number of different selections with at least 1 girl is 16.

 

Therefore, the answer is \rm C.

Related Problems
Problem 2 AMC 10 Weekly Practice Round 3
Problem 3 AMC 10 Weekly Practice Round 3
Problem 4 AMC 10 Weekly Practice Round 3
Problem 5 AMC 10 Weekly Practice Round 3
Think Academy Powered by ChatGPT