Tournament Matches Calculation
This problem involves calculating the total number of matches played in a tournament where every team plays every other team twice.
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Determine the number of teams involved. Let $n$ be the number of teams. Given: $n = 10$.
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Calculate the number of matches. Each team needs to play against the other $n-1$ teams. Since every team plays each of the other teams twice, we can calculate the total matches using the formula: Total Matches $= n \times (n-1)$
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Substitute the value of $n$ into the formula. Total Matches $= 10 \times (10-1)$ Total Matches $= 10 \times 9$ Total Matches $= 90$
Therefore, the total number of matches to be played is 90.
Important Questions from Combinations
Bob is studying the effect of coral and sponge species on reef ecosystems using experiments in artificial square tanks. In each tank, he places 3 species of corals and 2 species of sponges. If there are 6 species of corals and 5 species of sponges to choose from, the minimum number of tanks required to test all combinations of 3 coral and 2 sponge species is _______
(Answer in integer)
- There are nine species of Impatiens (balsams) found in laterite plateaus of the northern Western Ghats, each with a distinct colour. If a plateau has exactly 6 species, then the number of possible colour combinations in the plateau is __________. (Answer in integer)
- The number of ways in which a supervisor can choose four workers out of 10 equally competent workers is ________.
- In a box, there are 5 green balls and 10 blue balls. A person picks 6 ballsrandomly. The probability that the person has picked 4 green balls and 2 blueballs is
- There are 4 women P, Q, R, S, and 5 men V, W, X, Y, Z in a group. We are required to form pairs each consisting of one woman and one man. P is not to be paired with Z, and Y must necessarily be paired with someone. In how many ways can 4 such pairs be formed?
