taiwan-gsat 2023 Q4

taiwan-gsat · Other · gsat__math-a 5 marks Permutations & Arrangements Linear Arrangement with Constraints

Arrange the digits $1, 2, 3, \ldots, 9$ into a nine-digit number (digits cannot be repeated) such that the first 5 digits are increasing from left to right and the last 5 digits are decreasing from left to right. How many nine-digit numbers satisfy the conditions?
(1) $\frac{8!}{4!4!}$
(2) $\frac{8!}{5!3!}$
(3) $\frac{9!}{5!4!}$
(4) $\frac{8!}{5!}$
(5) $\frac{9!}{5!}$

Arrange the digits $1, 2, 3, \ldots, 9$ into a nine-digit number (digits cannot be repeated) such that the first 5 digits are increasing from left to right and the last 5 digits are decreasing from left to right. How many nine-digit numbers satisfy the conditions?\\
(1) $\frac{8!}{4!4!}$\\
(2) $\frac{8!}{5!3!}$\\
(3) $\frac{9!}{5!4!}$\\
(4) $\frac{8!}{5!}$\\
(5) $\frac{9!}{5!}$

Paper Questions

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