Suppose we have $2$ dice $(1,2,3,4,5,6)$ and we want to calculate the total number of unique combinations (order doesn't matter).
$n$ = number of values of dice
$r$ = length of output
I apply my formula for repeated unique combinations $C(n+r-1,r) = \dfrac {(n+r-1)!} {(n-r)! \, r!}$ and we get by substituting:
$C(7,2) = \dfrac {7!}{4! \, 2!}$ which is equal to $3 \times 5 \times 7$ which is $105$.However my textbook says the correct result is $21$.
Here are the careless mistakes:
$$C(n+r-1, r)=\frac{(n+r-1)!}{\color{red}{(n-1)}!r!}$$
$$C(7,2) = \frac{7!}{\color{red}5!2!}=\frac{7\cdot 6}{2}=21$$