A researcher wishes her patients to try a new medicine for depression. How many different ways can she select  5  patients from  47  patients?

In a town of 3,000 people, 600 are over 50 years of age and 400 are left-handed. It is also known that 15% of all left-handers in the town are over 50 years of age. How many people in the town are left-handed, over 50 years of age, or both?

There is a town party in Pleasantville where 6 families of 3 people each get together. If one representative from each family gives a gift to everyone at the party except people from their own family, how many gifts in total are given?

A doctor visits her patients during morning rounds. In how many ways can the doctor visit 8 patients during the morning rounds?

An interdepartmental task force is being formed to investigate an increase in violent crimes. 1/5 of the task force will be police officers from the local precinct. 1/4 will be ATF agents, and the remaining 22 will be from the FBI. How many people are participating in the task force?

Mr Chia purchased some colour files. 2/5 of them were red and the rest were blue. Mrs Lam bought 1/2 of the red and 1/3 of the blue ones from him. Mr Chia then found that he had 90 colour files left. How many colour files did Mrs Lam by altogether?