Difference between revisions of "Manuals/calci/BINOMIALCOEFFICIENT"

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#=BINOMIAL(32,0)= 1
#=BINOMIAL(32,0)= 1
#=BINOMIAL(10,7) = 120
#=BINOMIAL(10,7) = 120
==Related Videos==
{{#ev:youtube|v=07oNEAcZNko|280|center|Binomial coefficient}}
==See Also==
==See Also==

Latest revision as of 15:46, 27 November 2018


  • 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

Related Videos

Binomial coefficient

See Also