Let $f\left(n,k\right)$ denote the number of ways in which $k$ identical balls can be colored with $n$ colors so that there is at least one ball of each color. Then $f\left(2n,n\right)$ must be equal to a. ${}^{2}n{C}_n$ b. ${}^{2}n-1C_{n+1}$ c. ${}^{2}n-1C_n$ d. none of these

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