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.