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Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Hanlin writes down three $1$ s and three $0$ s, according to the following rule: while writing down the numbers, he must always have written at least as many $1$ s as he has written $0$ s. How many such numbers can he form from the six digits?

(A) $4$ (B) $5$ (C) $6$ (D) $7$ (E) $8$

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