You are organizing the first day of a local tennis tournament. You need to assig

Question

You are organizing the first day of a local tennis tournament. You need to assign 16 players to play eight singles matches on eight different courts. Below are three scenarios. For each one, determine the number of assignments you can make. You may use a calculator to find an answer, but your work should show any mathematical expressions being used.

a. You decide to select the pairings and assign them to the courts.

b. You select the pairings, but not the courts they will play on.

c. You decide to select the pairings, assign them to the courts, and determine who will serve first in each match.

Explanation / Answer

Solution

a) First pair can be selected out of 16, in 16C2 ways. Then, the next pair can be selected out of the remaining 14 in 14C2 ways. Continuing this way, total number of pair-selections will be:

16C2 x 14C2 x12C2 x …….. x2C2 which on simplification equals

[(16!)/{(2!)8}] [Using nCr = (n!)/{(r!)(n - r)!} ] …………………………………………..(1)

These 8 pairs can assigned to 8 courts in 8! Ways. Thus, number of assignments

= [(16!)/{(2!)8}] x (8!) ANSWER

b) As shown above, 8 pairs can be selected in [(16!)/{(2!)8}] ways. ANSWER

c) This is same as (a) with the additional condition of first server. The first server can be any one member of the pair. So, there are 2 possibilities. Thus, number of assignments

= 2 x [(16!)/{(2!)8}] x (8!) ANSWER

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