AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 9 Medium

There are 3 boys and 2 girls standing in a line. The two girls are not allowed to stand next to each other. Then there are            different possible arrangements.

Answer:72

For 5 people in a line, normally there are _{5}P_{5} = 120 arrangements.

If the two girls are adjacent, there are 2 \times _{4}P_{4} = 48 arrangements.

Therefore, the total number of arrangements is 120 - 48 = 72.

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