Question

An ice skating competition features 8 skaters. How many different ways can the skaters finish the competition? How many different ways can 3 of the skaters finish first, second and third?
need step by step explaination completely

Answer 1

Answer:

Statement of Purpose Read the personal details given below and prepare a suitable Statement of Purpose. Film and Television Institute of India

Answer 2

Given,

The ice skating competition features 8 skaters.

To find,

The different number of ways the skaters finish the competition and different ways in which  3 of the skaters finish first, second and third.

Solution,

We can simply solve the given question by using the concept of Permutations.

It is given that there an ice skating competition features 8 skaters.

Then by the Permutations, the different ways by which skaters can finish the competition is

                              = 8P8

                              = 8!

                              =40320

Now,  the different ways in which  3 of the skaters can finish first, second and third can be calculated by the formula,

                                         nPr = n!/(n-r)!

                                          8P3 = 8!/(8-3)!

                                                  = 8*7*6*5!/5!

                                                   = 8*7*6

                                                   = 336

Hence, the different ways in which the skaters can finish the competition is 40320 and the different ways in which 3 of the skaters can finish first, second and third is 336.