csat-suneung 2022 Q28 (Probability and Statistics)

csat-suneung · South-Korea · csat__math 4 marks Combinations & Selection Counting Functions or Mappings with Constraints

For two sets $X = \{ 1,2,3,4,5 \} , Y = \{ 1,2,3,4 \}$, how many functions $f$ from $X$ to $Y$ satisfy the following conditions? [4 points]
(a) For all elements $x$ in set $X$, $f ( x ) \geq \sqrt { x }$.
(b) The range of function $f$ has exactly 3 elements.
(1) 128
(2) 138
(3) 148
(4) 158
(5) 168

For two sets $X = \{ 1,2,3,4,5 \} , Y = \{ 1,2,3,4 \}$, how many functions $f$ from $X$ to $Y$ satisfy the following conditions? [4 points]\\
(a) For all elements $x$ in set $X$, $f ( x ) \geq \sqrt { x }$.\\
(b) The range of function $f$ has exactly 3 elements.\\
(1) 128\\
(2) 138\\
(3) 148\\
(4) 158\\
(5) 168

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