18 people enter a race, if there are no ties, how many ways can 1st, 2nd and 3rd place result?
There are 18 choices for first place, 17 for second, and 16 for third. Thus, there are 18*17*16=4896 ways.
Oh, the race for glory! With no ties allowed, we need to figure out the number of ways to determine the 1st, 2nd, and 3rd place. Since there are 18 people participating, let's break it down in a fun way:
For the 1st place, we have 18 options.
For the 2nd place, we have 17 options left (since one person already grabbed the gold medal).
For the 3rd place, we have 16 options remaining (since two champions are already crowned).
Now let's put on our math hat. To find the total number of ways, we need to multiply the number of options for each position:
18 (for 1st) * 17 (for 2nd) * 16 (for 3rd) = 4896 ways
So, there are 4896 possible ways to determine the 1st, 2nd, and 3rd place in this race. That's a whopping number of outcomes! Ready, set, go!
To determine the number of ways the 1st, 2nd, and 3rd place can result in a race with 18 people and no ties, you can use the concept of permutations.
In this case, you need to find the number of permutations of 18 people taken 3 at a time since you are looking for the ordering of the individuals.
The formula for permutations is:
P(n, r) = n! / (n - r)!
Where n is the total number of objects (people) and r is the number of objects (places) taken at a time.
In this case, you have 18 people and are selecting 3 at a time. So, the formula becomes:
P(18, 3) = 18! / (18 - 3)!
Calculating this:
P(18, 3) = 18! / 15!
Simplifying:
P(18, 3) = (18 x 17 x 16 x 15!) / 15!
The 15! on the numerator and denominator cancels out, and you are left with:
P(18, 3) = 18 x 17 x 16 = 4,896
Therefore, there are 4,896 ways the 1st, 2nd, and 3rd place can result in the race with 18 people and no ties.
To determine the number of ways the 1st, 2nd, and 3rd place can result in a race with no ties, we can use the concept of permutations.
In a race with 18 participants, the first place can be any one of the 18 participants. After the first place is determined, there are 17 remaining participants who can finish in second place. Finally, after the first two places are occupied, there are 16 participants left to finish in third place.
To find the total number of ways, we multiply the number of possibilities for each position together:
Number of ways = Number of possibilities for 1st place × Number of possibilities for 2nd place × Number of possibilities for 3rd place
Number of ways = 18 × 17 × 16
Number of ways = 4896
So, there are 4896 ways the 1st, 2nd, and 3rd place can result in the race.