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Calculate the probabilities of selecting at random: (a) the winning horse in a race in which ten horses are running, (b) the winning horses in both the first and second races if there are ten horses in each race.

A batch of 40 components contains five which are defective. A component is drawn at random from the batch and tested and then a second component is drawn. Determine the probability that neither of the components is defective when drawn (a) with replacement, and (b) without replacement.

A batch of 40 components contains five which are defective. If a component is drawn at random from the batch and tested and then a second component is drawn at random, calculate the probability of having one defective component, both with and without replacement.

A class has 24 students. Four can represent the class at an exam board. How many combinations are possible when choosing this group?

In how many ways can a team of 11 be picked from 16 possible players?