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Home » Unagi Sauce Is The Secret Ingredient Fueling the Trends You’re Missing! - Appcentric

Unagi Sauce Is The Secret Ingredient Fueling the Trends You’re Missing! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Thus, there are 1260 distinct token sequences.

📌 oxed{1260}

📌 Question: A science educator assigns 7 unique digital badgesâ3 for Robotics, 2 for Coding, and 2 for Data Scienceâto students over a week, one badge per day. If the badges within each category are indistinguishable, how many distinct daily sequences can be created?

📌 Solution: We are arranging 7 badges where 3 are identical Robotics (R), 2 are identical Coding (C), and 2 are identical Data Science (D). The number of distinct sequences is the multinomial coefficient:

📌 rac{7!}{3! \cdot 2! \cdot 2!}

📌 $ 7! = 5040 $

📌 $ 3! = 6 $, $ 2! = 2 $, so denominator = $ 6 imes 2 imes 2 = 24 $

📌 rac{5040}{24} = 210

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Point to project: \(\mathbf{p} = egin{pmatrix} 5 \ 4 \end{pmatrix}\)
Vector from point on line to \(\mathbf{p}\):
\mathbf{v} = \mathbf{p} - \mathbf{r}_0 = egin{pmatrix} 5 - 1 \ 4 - (-...
Project \(\mathbf{v}\) onto \(\mathbf{d}\):
ext{proj}_{\mathbf{d}} \mathbf{v} = \left( rac{\mathbf{v} \cdot \math...
ight) \mathbf{d}
Compute dot products:
\mathbf{v} \cdot \mathbf{d} = 4 \cdot 3 + 6 \cdot 1 = 12 + 6 = 18
\mathbf{d} \cdot \mathbf{d} = 3^2 + 1^2 = 9 + 1 = 10
Projection scalar:

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