Of all the mappings that can be defined from the set A : {1,2,3, 4} $\to$ B : {5, 6,7 ,8, 9} , a mapping is randomly
selected. The chance that the selected mapping is strictly monotonic is

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Infinity Learn · Accepted Answer

Each $$pre-image$$ in set A can be assigned any one of the $$5$$ images from set B Hence total number of functions are $$n(S)=54=625$$ For strictly monotonic function either function is increasing or decreasing. For which four different images are used, which can be selected  $$5C4way$$. Hence number of monotonic functions are $$n(A)=2$$⋅$$5C4=10$$ (either$$ increasing or $$decreasing) ∴ $$P(A)=10625=2125$$

Of all the mappings that can be defined from the set A : {1,2,3, 4} $\to$ B : {5, 6,7 ,8, 9} , a mapping is randomly
selected. The chance that the selected mapping is strictly monotonic is

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Of all the mappings that can be defined from the set A : {1,2,3, 4} → B : {5, 6,7 ,8, 9} , a mapping is randomlyselected. The chance that the selected mapping is strictly monotonic is

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Of all the mappings that can be defined from the set A : {1,2,3, 4} $\to$ B : {5, 6,7 ,8, 9} , a mapping is randomly
selected. The chance that the selected mapping is strictly monotonic is