what is the MATLAB function to evaluate ncr value when n is real

what is the MATLAB function to evaluate ncr value when n is real

[Kaushik Lakshminarasimhan]

What is ncr?

[Walter Roberson]

Number of combinations??

You can easily transform the traditional factorial definition of combinations to use the GAMMA function, but as soon as you go for negative values you have a problem that GAMMA of negative values is infinite.

[PJS KUMAR]

formula to find number of different combinations of n distinct objects taken r at a time

[Walter Roberson]

What result are you expecting for nCr(-3,pi) ?

[PJS KUMAR]

expecting result for instances like nCr(0.5,2) , nCr(-3,2)

[Walter Roberson]

What numeric values do you expect for the cases nCr(0.5,2) and nCr(-3,2) ? Number of combinations is only defined for positive integers.

Answer 1

[Kaushik Lakshminarasimhan]

If n and r are both non-negative integers, and n >= r, use:

nCr = nchoosek(n,r)

If n and/or r can be negative, you can use the more general form:

nCr =  gamma(n+1)/(gamma(r+1)*gamma((n-r)+1))

If either n or r is an integer <= -1, then the nCr is not defined.