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 isA. `(1)/(125)`B. `(2)/(125)`C. `(3)/(25)`D. `(6)/(25)`

Of all the mappings that can be defined from the set `A :{1,2,3,4} to

1.	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 isA. `(1)/(125)`B. `(2)/(125)`C. `(3)/(25)`D. `(6)/(25)`
Answer» Correct Answer - B `(b)` 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)=5^(4)=625` For strictly monoatonic function either function is increasing or decreasing. For which four different images are used, which can be selected in `"^(5)C_(4)` way. Hence number of monoatomic functions are `n(A)=2*"^(5)C_(4)=10` (either increasing or decreasing) `:. P(A)=(10)/(625)=(2)/(125)`

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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 isA. `(1)/(125)`B. `(2)/(125)`C. `(3)/(25)`D. `(6)/(25)`

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