Suppose you have a regular die with 6 faces numbered 1 through 6, respectively, and roll the die 4 times. What is the probability that the sum of the 4 rolls is 14?
This problem is equivalent to asking the number of ways to partition the number 14 into 4 subsets using 6 different numbers. Hence we can consider 'multichoosing' 4 numbers with repetition out of 6 different numbers such that $14 = x_1 + x_2 + x_3 + x_4$. I suspect that this can be done using either using multinomial coefficients in some way or multisets but I am not entirely sure. One issue is that this does not give a way for removing those cases where the four number chosen $\ne$ 14.
The total number of outcomes from rolling a die 4 times is $6^4$, so our probability will be some number divided by this.
Is this likely a problem where I should just enumerate all possible options to find my numerator?