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  • 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

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See Also