In order for there to be an injection from it must be the case that .
Then we count the number of permutations of taken at a time: .
In terms of probability .
Let S be the set of all functions from {1, 2} to {1, 2, 3}. Let F be an element of S chosen at random.
Find |S| and find the probability that F is an injective function.
For the question I know the |S|= 9 but finding it difficult to find the probability that f is an injective function.
Let S be the set of all functions from {1, 2, 3} to {1, 2}. Let G be an element of S chosen at random.
Find |S| and find the probability that G is an injective function.
For the question I know that the probability that f is an injective function is 0 as this can not be injective as the domain and co domain is disjoint. But I am finding it difficult to find |S|.
Let S be the set of all functions from {1, 2,…, M} to {1, 2,…, N}. Let Q be an element of S chosen at random.
Find |S| and find the probability that Q is an injective function.
For this question I do not understand it at all.
Thanks for for the help. I do understand the first part and what is meant by injective but i do not understand about the following:
Then we count the number of permutations of taken at a time: .
In terms of probability and the question.
Can you please explain it to me in more detail.
Thanks
The1u2001