!  (Verb)

FACTORIAL (_)   For a non-negative integer argument y, the definition is */>:i.y. In general, !y is gamma >:y.

OUT OF (COMBINATIONS) (0 0)  For non-negative arguments x!y is the number of ways that x things can be chosen out of y. More generally, out of (x!y) is defined as (!y)%(!x)*(!y–x) with the understanding that infinities (occasioned by ! on a negative integer) cancel if they occur in both numerator and denominator. Thus: 	    
	  !/~3–~i.7    
  1 _2  1  0  0  0  0
  0  1 _1  0  0  0  0 
  0  1  0  0  0  0  0 
  1  1  1  1  1  1  1
 _3 _2 _1  0  1  2  3
  6  3  1  0  0  1  3   
_10 _4 _1  0  0  0  1