Six sprinters have qualified for the finals in the 100-meter dash at the NCAA national track meet. In how many ways can the sprinters come in first, second, and third?
(Let's assume there are no tires).
Well, as a Clown Bot, I'm not really a speed expert, but I can definitely calculate some humorous probabilities for you. Since there are six sprinters and three different positions (first, second, and third), we can think of this as a clown car race! In a clown car, you never know who's going to come out first, second, or third - they keep popping out from all over the place!
If we take a moment for clown confetti and assume that no two sprinters can cross the finish line at the same time (because that would just be chaos), then we can use a little math to figure it out:
For the first position, any of the six sprinters can come in first. So we have 6 choices. Once we've got that sorted, there are only 5 sprinters left to choose from for the second position. And finally, there are 4 sprinters left to choose from for the third position.
So, using clown math (also known as basic counting principles), we multiply the number of choices together: 6 x 5 x 4 = 120.
Therefore, there are 120 different ways these sprinters can come in first, second, and third. Just keep in mind that this might change if a clown car suddenly appears on the track!
To determine the number of ways the sprinters can come in first, second, and third, we can use the concept of permutations.
Since there are 6 sprinters, there are 6 possibilities for the first-place finisher. Once the first-place finisher is determined, there are 5 remaining sprinters who can finish second. Finally, after determining the first and second-place finishers, there are 4 remaining sprinters who can finish third.
Thus, the number of ways the sprinters can come in first, second, and third is:
6 x 5 x 4 = 120
Therefore, there are 120 different ways the sprinters can come in first, second, and third.
To find the number of ways the sprinters can come in first, second, and third, we can use the concept of permutations.
In this case, we need to find the number of permutations of 6 objects taking 3 at a time, because we want to determine the order in which the sprinters finish.
The number of ways to arrange 6 objects taking 3 at a time (without repetition) is denoted as P(6, 3) and can be calculated using the formula:
P(6, 3) = 6! / (6 - 3)!
where "!" represents the factorial of a number.
The factorial of a number n (denoted as n!) is the product of all positive integers from 1 to n.
Using the above formula, we can calculate the number of ways as follows:
P(6, 3) = 6! / (6 - 3)!
= 6! / 3!
= (6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1)
= 6 * 5 * 4
= 120
Therefore, there are 120 ways the sprinters can come in first, second, and third in the 100-meter dash.
6 sprinters 3 at a time but ORDER matters
so we are talking permutations not combinations
n!/(n-r)! = 6!/3! = 6*5*4 = 120