Question
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)?
Answers
Answered by
GPT 3.5
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.
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.