# Difference between revisions of "Manuals/calci/BINOMIAL"

BINOMIAL(N,K)

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

## Description

• 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.

## ZOS

• 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)

## Examples

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

BINOMIAL