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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Permutation and Combination

Olympiad workbook · IOQM · Permutation and Combination

Find the number of maps f:\ 1,2,3\ arrow\ 1,2,3,4,5\ such that f(i)...

Find the number of maps f:{1,2,3}→{1,2,3,4,5}f:\{1,2,3\} \rightarrow\{1,2,3,4,5\} such that f(i)≤f(j)f(i) \leq f(j) whenever i<ji < j

Correct answer

35

Step-by-step solution

\begin{array}{ll}f(i) \leq f(j) & i < j \\ \left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right) & \left(12345\begin{array}{l}1 \\ 2 \\ 3 \\ 4 \\ 5\end{array}\right)\end{array} y1+y2+y3+y4+y5=33+4C4=7C4=35\begin{aligned} & y_1+y_2+y_3+y_4+y_5=3 \\ & { }^{3+4} C_4={ }^7 C_4=35\end{aligned}
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