Given 10 iid random variables where each of them takes value from a set of 6 constants.

$$ M\_i \in \left\{0, 0.06, 0.07,0.08,0.09,0.1\right\} \quad \text{for} \: i = 1,...,10$$

$$ S = \sum\_{i=1}^{10} M\_i$$

How can I find the number of all possible outcomes of their sum $S$? Please explain the logic.

EDIT: I have tried to solve this problem using brute force in python, here are my results:

```
[IN]
M = [0, 0.06, .07, .08, .09, .1]
S = []

for a in M:
    for b in M:
        for c in M:
            for d in M:
                for e in M:
                    for f in M:
                        for g in M:
                            for h in M:
                                for i in M:
                                    for j in M:
                                        dummy = a+b+c+d+e+f+g+h+i+j
                                        S.append(dummy)
print(len(S))             
print(len(list(set(S))))

[OUT]
60466176
291

```

Apparently, the answer to my question is 291. Could anyone help me explain this please?