# Balanced incomplete block design

1. Apr 28, 2010

### Philip Wong

hi,
I've got an balanced incomplete block design, and I want to work out the efficiency of this design. In order to work out the efficiency I implied the following equations:
r=b*k / t
lambda = r(k-1)/ t-1
e= t*lambda / r*k

I got into a cliche of which to use to work out what to use for block (b), the cliche are:
compared three of eight different varieties of beer (i.e. 8 choose 3)

1) is block 8*3
2) is block 8chose 3, if so how can I work it out? hence I don't have a graphic calculator

thanks!

2. Apr 28, 2010

### Philip Wong

alright I take that back! I just worked it out!
the equation you would used to work out how many blocks are there for BIBD is:

"a" choose "b" (i.e. 8 choose 3 in my case)
then: a!/k!(a-k)!
so: 8!/(3!*(3-8)!)

where ! just meant, a chain of multiplication. i.e. for 8! it would be 8*7*6*5*4*3*2*1, while 3! would be 3*2*1, and -5! would be -5*-4*-3*-2*-1