Thus, there are 1260 distinct token sequences.

February 22, 2026

Thus, there are 1260 distinct token sequences.

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$ 4! = 24 $, $ 3! = 6 $, $ 2! = 2 $
Denominator: $ 24 imes 6 imes 2 = 288 $
rac{362880}{288} = 1260
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:

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