I am trying to determine the total number of possible combinations of elements for the following vectors:
F1=c("0","1","2","3","4"),
F2=c("0","1","2"),
F3=c("0","1","2"),
F4=c("0","1","2"),
F5=c("0","1","2"),
F6=c("0","1","2","3","4","5"),
F7=c("0","1","2","3"),
F8=c("0","1","2"),
F9=c("0","1","2","3"),
F10=c("0","1","2","3","4"),
F11=c("0","1","2","3","4"),
F12=c("0","1","2"),
F13=c("0","1","2"),
F14=c("0","1","2"),
F15=c("0","1","2"),
F16=c("0","1","2"),
F17=c("0","1","2")
Specifically, I am interested in knowing the number of combinations that have exactly 10 elements greater than 0 (and by necessity the other 7 elements are exactly 0). Does anybody know of a general method (formula) that could be used to solve this problem?