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2022 AMC 8 Question 23

AMC8 · 2022 AMC 8

Question 23

A $\bigtriangleup$ or $\bigcirc$ is placed in each of the nine squares in a $3 \times 3$ grid. Shown below is a sample configuration with three $\bigtriangleup$’s in a line.

Question illustration

How many configurations will have three $\bigtriangleup$’s in a line and three $\bigcirc$’s in a line?
  1. $39$
  2. $42$
  3. $78$
  4. $84$
  5. $96$