Twenty players compete in a tournament In how many ways can

Twenty players compete in a tournament. In how many ways can rankings be assigned to the top five competitors? In how many ways can the best five competitors be chosen (without being in any order)?

Solution

number of ways ranking can be assigned to top 5 contributors

= 20 * 19 * 18 * 17 * 16 = 20P5 = 1860480

b)

number of ways 5 best competetors can be choosen

= 20 C 5

= 15504