Difference between revisions of "Manuals/calci/BINOMIALCOEFFICIENT"

From ZCubes Wiki
Jump to navigation Jump to search
Line 41: Line 41:
[[Z_API_Functions | List of Main Z Functions]]
*[[Z_API_Functions | List of Main Z Functions]]
[[ Z3 |  Z3 home ]]
*[[ Z3 |  Z3 home ]]

Revision as of 00:58, 13 March 2017


  • 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.


  1. =BINOMIAL(10,3)= 120
  2. =BINOMIAL(32,0)= 1
  3. =BINOMIAL(10,7) = 120

See Also