Let X and Y denote the sets containing 2 and 20 distinct objects respectively and F denote the set of all possible funct...

Question

Let X and Y denote the sets containing 2 and 20 distinct objects respectively and F denote the set of all possible functions defined from X to Y. Let f be randomly chosen from F. The probability of f being one-to-one is ______.

Accepted Answer

0.95 X has 2 elements and Y has 20 elements. A function from X to Y assigns each element of X to some element of Y. Out of all such functions, we want those that are one-to-one (injective), meaning no two elements of X map to the same element of Y. Probability = (number of injective functions) / (total functions).