Combination with repeatation formula

[rajeshmarndi]

Homework Statement

The combination of n different object, taken r at a time(repeatation allowed) is given by
Cⁿ_r = (n-1+r)! / [(n-1)! r!]

Homework Equations

The Attempt at a Solution

The above formula is deducted, as it is same as no. of ways of placing n-1 bar in n-1+r places, which is same as combination (repeatation not allowed) of n-1 object placed in n-1+r places. But permutation and combination formula or online calculator doesn't allow when r>n, (r= place, n= no. of objects). Then how is the prove of the above formula deducted?

Also the above formula is similar to combination(repeatation not allowed) of n-1+r object placed in r places.

 

[haruspex]

The combination of n different object, taken r at a time(repeatation allowed)

"At a time" should not be used when describing combinations that allow repetition. See e.g. http://en.wikipedia.org/wiki/Combination.

calculator doesn't allow when r>n

Does your calculator have separate functions for with and without repetition? If it does, you must be selecting the wrong one. If it does not, you must do the n+r-1 calculation separately and plug that into the function as 'n'.