Statistics homework. Thank you (a) Six tennis players have signed-up for a round
ID: 3271866 • Letter: S
Question
Statistics homework. Thank you
(a) Six tennis players have signed-up for a round-robin tennis tournament. The first set of 3 matches will be played at Sam on Saturday and one possible game set-up follows: 1-6 2-5 3-4 Because there is no distinction in the 3 courts where games are played (i.e. what really matters is who plays each other), note that the following set-up is considered the same as the example above: 6-1 4-3 2-5 In how many unique ways can the first set of 3 matches be assigned? Provide an answer that utilizes permutations and/or combinations. (b) (Continuing from 2A-2 a) Suppose there had been 8 tennis players? In how many unique ways can the first set of 4 matches be assigned? (Assume there are 4 indistinguishable courts.)Explanation / Answer
1) We acn select the first pair by 6C2 2nd pair by 4C2 and last pair by 2C2 so the ways are = 6C2*4C2*2C2 / 3!
divided here by 3! since the order doesn't matter here
ans= 15
2) Same way for 4 pairs ans= 8C2 * 6C2 * 4C2 * 2C2 / 4! = 105
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