It is apparent that, as n grows large, the factorial n! can be astronomical. For instance, 20! is about 2.43 × 1018, while 100! is around 9.3 × 10157. Mathematica can be used to find the binomial coefficients

(n k

)

. For the number of combinations of k elements out of n (i.e. for the binomial coefficients), the command Binomial can be used directly. For instance, In[1]:= 25!

Out[1]= 15511210043330985984000000 In[2]:= 50!/40!

Out[2]= 37276043023296000 In[3]:= Binomial[30,10]

Out[3]= 30045015