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

Options

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

Answer

B

Explanation

`(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)`