Question

54 people are competing in an athletic event. the top 4 competitors receive prize money, with 1st being worth more than 2nd, 2nd worth more than 3rd, etc. how any ways can the 4 prizes be given

Answer 1

There are 249,900 ways the 4 prizes can be given to the competitors.

Step-by-step explanation:

To determine the number of ways the 4 prizes can be given to the competitors, we will use the concept of permutations. Since the order of the prizes matters, we will use the formula for permutations. The formula for permutations is P(n, r) = n! / (n-r)!, where n is the total number of competitors and r is the number of prizes to be given.

Using the formula, we can calculate the number of ways as follows:

P(54, 4) = 54! / (54-4)! = 54! / 50! = (54 * 53 * 52 * 51) = 249,900

Therefore, there are 249,900 ways the 4 prizes can be given to the competitors.

Answer 2

To calculate the number of ways the 4 prizes can be given out among 54 competitors, use the permutation formula 54P4, resulting in a product of 54 x 53 x 52 x 51.

Step-by-step explanation:

In the athletic event with 54 competitors where the top 4 competitors receive prize money and each prize is of different value, we need to calculate the number of ways the 4 prizes can be given out. This can be done using permutations since the order in which we give out the prizes matters. We want to arrange 4 unique prizes among 54 people.

To determine the number of ways to do this, we use the formula for permutations, which for selecting r items from a set of n is given by nPr = n! / (n-r)!. Here, we have n = 54 people and we want to choose r = 4 winners.

Thus, the number of ways to award the prizes can be calculated as follows:
54P4 = 54! / (54-4)!
This simplifies to 54 x 53 x 52 x 51, since the factorials cancel out leaving only the product of the first 4 numbers.