Each of the six players participating in a chess competition will play one match with each other player. Tell us how many matches will be played in the entire competition-a)30b)36c)15d)12Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Given:

Each of the six players participating in a chess competition will play one match with each other player.

Concept Used:

ⁿC_r = n!/r!(n - r)!

Calculations:

Symbolically, this can be represented as C(n, r) where:

n represents the total number of players.
r represents the number of players in a single match.

In this case, n is 6 (the total number of players) and r is 2 (players in a single match).

So, in the notation of combinations, the number of matches would be represented as C(6,2).

C(6,2) = 6! / [2!(6-2)!] = 30/2 = 15

∴ There will be 15 matches played in the entire competition.

Answer

Calculating the number of matches in a chess competition:

- Each player will play one match with each of the other five players.
- Therefore, for each player, there will be 5 matches in total.

Total number of matches:

- Since there are 6 players in the competition, we need to calculate the total number of matches played by all players combined.
- This can be done by multiplying the number of matches each player plays (5) by the total number of players (6).
- So, the total number of matches in the entire competition will be 5 * 6 = 30 matches.

Correct answer:

- The correct answer is option 'C' which states that there will be 15 matches in the entire competition.
- This is because the question asks for the number of matches played, not the total number of match opportunities.
- Each match involves two players, so when we divide the total number of matches (30) by 2, we get the actual number of matches played, which is 15.

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