Question

Determine the counting method you could use to solve the given counting problem: At a golf tournament, 5 door prizes will be awarded to the competing golfers. If 44 golfers have entered the tournament, in how many ways can the 5 prizes be awarded? Assume no golfer can win more than one door prize and that the prizes will be given in order of 1st, 2nd, 3rd, etc.

1) Permutation
2) Combination
3) Factorial
4) Probability

Answer 1

The counting method used to determine the awarding of 5 prizes to 44 golfers is permutation, as order is important and each golfer can only win once. The calculation is 44! / 39!.

Step-by-step explanation:

To determine the counting method to solve the problem of awarding 5 door prizes to 44 competing golfers, we look for an arrangement where order matters, and no golfer can win more than one prize. This is a permutation problem because each of the 5 prizes is distinct (1st, 2nd, 3rd, etc.) and being awarded to a different person.

To solve this, use the permutation formula, which is P(n, k) = n! / (n-k)!, where 'n' is the total number of items, and 'k' is the number of items to choose. Here, n is 44 and k is 5.

The calculation would therefore be 44! / (44-5)!, which simplifies to 44! / 39!. This will give you the total number of ways the 5 prizes can be awarded among the 44 golfers.