Question

How many different ways can a race with 7 runners be completed?

Answer 1

Answer:

Just for the reason that, you do not have any further doubt on this.

If you have studied Permutations & Combinations or Combinatorics, you will know, actually, the 1st, 2nd and 3rd places can be selected in 7P3 or (73)×3!. Here, what we are doing is, we are finding the number of ways of choosing 3 elements from the 7 given elements to be our 1st, 2nd and 3rd place holders and since the order matters here, i.e., how the 3 chosen elements are arranged to be 1st, 2nd and 3rd matters here, we multiply it by 3!.

Answer 2

Answer:

as given we have to find number of ways can a race with 7 runners be completed it is completed in 7! = 7*6*5*4*3*2*1 = 5040 ways

Step-by-step explanation: thats a lot of ways