If you go to previous versions and look at the first one, 02/15/2001, which is yours?, you will see :
1). q (1-p), maybe a typo?
2). And the formula for the numbers of ways of picking X items out of N items was:
N!/X!/(N-X)!. This is plain wrong. Yes, after requesting a change for a week, I changed it.
3).There were also wording problems. RoseParks.
I see now the problem. (1-p) was intended as a parenthetical definition. I guess N1/X!/(N-X)! worked in my programming codes so I couldn't see the ambiguity. How would you calculate N!/X!/(N-X)!? From right to left? On the other hand, Today is 02/20/2001, so I think your "requesting a change for a week" is a bit off. Today is only the 20th by my calendar. In any case, the criticism has led to something better.
Dick Beldin
In answer to your question on how you evaluate, N!/X!/(X-N)!, this is ambiguous. In any easy example.
2/4/12 is ambiguous since
- (2/4)/12= 2/48=1/24 while
- 2/(4/12)= 24/4= 6.
Multiplication is associative over the reals. If you look at division as the inverse operation of multplication, i.e. 2/4/12=2*4^1*12^1=1/24 you are okay. If you look at division in the ordinary sense, you must specify the order of operations.
RoseParks
I agree that an expression with successive divisions appears ambiguous. Most mathematicians I know do indeed consider division as the inverse of multiplication and many programming languages explicitly specify that multiplication and divisions are performed left to right. You are correct, it is not a universal convention. In addition, the vertical placement of numerator and denominator is clearer.
Dick Beldin
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