Each week Bob and three friends from work pool their money together and buy 12 lottery tickets that are randomly and equally divided among the group. By luck, there are two winning tickets among the 12 tickets purchased by Bob and his friends. What is the probability that different people end up with these winning tickets?
A general is planning to invade towns A, B, C and has 20 soldiers at his disposal (6 officers and 14 privates). After some thought, the general decides to select 12 soldiers to carry out the invasion and to keep the remaining 8 (and himself) behind to protect the command post. If the general takes 12 selected soldiers (3 officers and 9 privates), and randomly selects 4 soldiers w/o replacement, to invade towns A, B, C, what is the probability that exactly one officer ends up being sent to each town?