how to answer this using permutations and combinations

1. Fourteen runners join a race. In how many possible ways can they be arranged as
first, second and third placers
2. A car manufacturer sells 5 models of cars in 7 colors with either manual or automatic
transmissions. How many variations does the manufacturer offer?
3. How many different 3-digit even numbers can be drawn from the digits 1, 3, 5, 6, 8
and 9 if no repetition of digits is allowed?
4. In how many ways can 12 people be seated around a circular table if three of them
insist on sitting beside each other?
5. From a group of 15 scholars, in how many ways can a university sent 4 of them to a
conference?
6. A box contains 16 red and 14 blue marbles. In how many ways can 9 red and 7 blue
marbles be chosen?
7. A club with 20 members will elect their officers, in how many ways can they choose a
president, a vice president, a secretary, and a treasurer?
8. In how many ways can you place 9 different books on a shelf if there is space
enough for only 5 books?
9. If there are 10 people and only 6 chairs are available, in how many ways can they be
seated?
10. In a gathering, the host makes sure that each guest shakes hands with everyone
else. If there are 30 guests, how many handshakes will be done?