Permutations and Combinations Exam Pattern Mix

In how many ways can gold, silver and bronze medals be awarded among 10 athletes?

A president and a secretary are chosen from 10 members, but member A will not serve as secretary. In how many ways?

A polygon has three times as many diagonals as sides. How many sides does it have?

How many triangles can be formed by joining the vertices of a 12-sided polygon?

At a party of 15 people (6 married couples and 3 single people), everyone shakes hands with everyone except their own spouse. How many handshakes are there?

In a league of 12 teams, every team plays every other team twice (home and away). How many matches are played?

A knockout tournament starts with 32 teams. How many matches are played in all?

In how many ways can 6 different books be given to 3 students so that each gets 2?

In how many ways can 6 different books be tied into 3 bundles of 2 books each?

In how many ways can 3 letters be dropped into 5 post boxes?