Question

Hey, guys, I was wondering if you could help me with some statistics and physics. http://www.trin.cam.ac.uk/show.php?dowid=475 Questions 2, 4, 5, 6, 9 and 10.

Answer 1

4) 2n players must be 2n-1 pairings, i.e., 1*3*5*...*(2n-1)=
=(2n-1)!/(2*4*6*...*(2n-2))
=(2n-1)!/(2^(n-1)*1*2*3*...*(n-1))
=(2n-1)!/(2^(n-1).(n-1)!)

Answer 2

Could you explain it in more detail?

Answer 3

2) this is an example of Bayes rule. Here's a detailed wikipedia example with different numbers: http://en.wikipedia.org/wiki/Bayes'_theorem#Drug_testing

Answer 4

I had my professor explain this. He says it is one of the fundamental concepts in counting or combinatorics. It might be clearer to see it with smaller numbers, 8 players must have 7 pairings.
7.5.3.2.1=\[\frac{ 7.(6).5.(4).3.(2).1 }{ 6.4.2 }\](The even numbers drop in the denominator.)\[=\frac{ 7! }{ 2^{3}.(3.2.1) }\]=\[\frac{ 7! }{ 2^{3}.3! }\]