From ZCubes Wiki
Revision as of 05:59, 9 March 2017 by Jayaram (talk | contribs)
Jump to navigation Jump to search

  • is the number of items.
  • is the number of selection.


  • This function gives the coefficent of the binomial distribution.
  • Binomial coefficient is the set of positive integer which equals the number of combinations of k items that can be selected from a set of n items.
  • The coefficients satisfy the Pascals recurrence.
  • The binomial coefficents are denoted by and it is read by n choose k.
  • It is the coefficient of the term in the polynomial expansion of the binomial thorem .
  • The coefficient is occur in the formula of binomial thorem:
 where . 
  • To find the coefficient of the binomial ,we can use several methods.
  1. Recursive formula 
  2. Multiplicative formula 
  3. Factorial formula.
  • 1.Recursive Formula:
  for  and .
  • 2. Multiplicative formula:

  • 3.Factorial formula:

where ,and which is zero when .

  • Also for the initial values for .
  • Most compact formula for the coefficient of the binomial value is Factorial formula.
  • Factorial formula is symmetric of the combination formula.


  • The syntax is to calculate BINOMIAL in ZOS is .
    • is the number of items.
    • is the number of selection.
  • For e.g., BINOMIAL(20..25,4)
  • BINOMIAL(10..14,7..8)


  1. =BINOMIAL(10,3)= 120
  2. =BINOMIAL(20,7)= 77520
  3. =BINOMIAL(15,0)= 1
  4. =BINOMIAL(12,12)=1
  5. =BINOMIAL(1,-1) = 0

Related Videos


See Also


List of Main Z Functions

Z3 home