14 wrestlers compete in a competition .if each wrestler wrestles one match each with each other wrestler ,what are the total numbers of matches.
Each of the 14 wrestlers has 13 matches.
So, that makes 14*13 = 182 matches.
But, if that were true, each wrestler would have met the others twice
(10 vs 12 is the same as 12 vs 10) so divide by 2.
91 matches
This is the same as 1+2+3 + ... +13
Well, when you have 14 wrestlers who each wrestle one match with every other wrestler, it's like a giant wrestling roulette wheel! Each wrestler goes head-to-head with the other 13 wrestlers, excluding themselves of course (we don't want any self-wrestling mishaps!). So, we need to calculate the number of ways we can pair up these wrestlers.
To do this, we use a classic formula: (n*(n-1))/2. Plugging in our number of wrestlers, n=14, we get:
(14 * (14-1))/2 = 91
So, grab some popcorn and a comfy seat because there will be 91 matches in total! That's enough wrestling action to keep you entertained for quite a while. Enjoy the show!
To determine the total number of matches, we can use the formula for finding the number of combinations.
The formula for finding the number of combinations is given by nC2 = n! / (2!(n-2)!)
Here, n is the number of wrestlers, which is 14.
So, substituting the value of n into the formula:
14C2 = 14! / (2!(14-2)!)
= 14! / (2!12!)
= (14 * 13 * 12!) / (2!12!)
= (14 * 13) / 2!
= 182 / 2
= 91
Therefore, there will be a total of 91 matches.
To find the total number of matches when 14 wrestlers compete in a competition, we can use the concept of combinations.
When there are n wrestlers, each wrestler needs to compete with every other wrestler exactly once. In a single match, two wrestlers compete against each other. So, for one match, we need two wrestlers.
To form a match, we can choose 2 wrestlers out of the total 14 wrestlers. This can be represented as choosing 2 wrestlers from a set of 14 wrestlers, which is denoted as "14 choose 2" or written as C(14, 2).
The formula for combinations is:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of items and r is the number of items we want to choose.
In our case, n = 14 and r = 2. Plugging these values into the formula, we get:
C(14, 2) = 14! / (2! * (14-2)!)
Simplifying further:
C(14, 2) = 14! / (2! * 12!)
= (14 * 13 * 12!) / (2 * 1 * 12!)
Canceling out the common terms:
C(14, 2) = (14 * 13) / (2 * 1)
= 182 / 2
= 91
Therefore, the total number of matches when 14 wrestlers compete in a competition is 91.