To find the number of objects in a population when given r and the number of combinations nCr, one can use the binomial coefficient formula _{n}C_{r}. There is no straightforward formula for determining n from C and r; instead, it involves factoring and ensuring that C is a valid binomial coefficient. A practical approach is to start searching from n=r and apply the recurrence relation (n+1)Cr = nCr*(n+1)/(n+1-r). This method guarantees a solution if it exists, as the terms increase. Understanding combinations and permutations is crucial for accurate calculations.
