There are 50 competitors in the men’s ski jumping competition. 30 move on to the qualifying round. How many different top 30 finishes can there be (order matters)?

Answer 1

Since order matters, the number of different top 30 finishes can be found using permutations.

The formula for permutations is P(n, r) = n! / (n-r)!

In this case, there are 50 competitors and 30 spots, so we would use the formula P(50, 30).

P(50, 30) = 50! / (50-30)!
= 50! / 20!

Calculating this would be computationally expensive, but you can simplify it by canceling out some terms.

P(50, 30) = (50 * 49 * 48 * 47 * ... * 21 * 20!) / 20!

Notice that the 20! terms cancel out.

P(50, 30) = 50 * 49 * 48 * 47 * ... * 21

Using a calculator or a computer program, you can multiply these numbers together to find the total number of different top 30 finishes.

P(50, 30) ≈ 483,062,599,661,420,032,744,898,560,000

Therefore, there can be approximately 483,062,599,661,420,032,744,898,560,000 different top 30 finishes in the men's ski jumping competition.