Question

If A ={1,2,3,4} and B={1,2,3,4,5,6} and f:A to B is an injective mapping satisfying f(x) is not equal to x number of such mapping possible are?

Answer 1

Given-:

Two sets A={1,2,3,4} & B= {1,2,3,4,5,6,} such that f: A to B is an injective mapping satisfying f(x) is not equal to x

To Find-:

The no. of possible injective mapping

Solution-:

• As we know that injective mapping defined as the one one mapping means all the elements in domain (preimage) have distinct images in codomain (image)

• And here in this case we have domain= {1,2,3,4} having 4 elements Whereas the codomain ={1,2,3,4,5,6,} having 6 elements .The first element in domain have 6 images in codomain , 2nd element have 5 images , 3rd have 4, 4th have 3 images respectively  

So the total no. of injective mapping possible = 6*5*4*3 = 360