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📅 May 12, 2026 👤 scraface

May 12, 2026

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📌 Solution: First, calculate the total number of ways to choose any 4 samples from the 13 total (8 viral strains + 5 control samples):

📌 \binom{13}{4}

📌 Now subtract the number of selections that include only control samples (i.e., no viral strain):

📌 \binom{5}{4}

📌 So, the number of valid sequences with at least one viral strain is:

📌 \binom{13}{4} - \binom{5}{4} = 715 - 5 = 710

📌 Thus, the number of ways to select such a sequence is $\boxed{710}$.

📌 Question: A robotics engineer is programming a robot to navigate a grid that is 5 rows by 5 columns. If the robot starts at the bottom-left corner and must move only right or up to reach the top-right corner, how many distinct paths avoid the center square at (3,3)?

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