# Tag Info

Accepted

### Let $x_i \in \mathbb Z,$ such that $|x_1|+|x_2|+|x_3|+...+|x_{10}|=100.$ Find number of solution.

Let $r$ be the number of zeros in $x_1,x_2,\cdots, x_{10}$ where $0\le r\le 9$. There are $\binom{10}{r}$ ways to choose $r$ zeros in $x_1,x_2,\cdots,x_{10}$. The number of non-zero $x_i$ is $10-r$. ...
• 141k
Accepted

### Simple solution to random walk

One way to solve this problem is to represent the possible courses of the match by paths through a directed graph. Each vertex of the graph represents a possible score $\ (h,a)\$ that might have ...
• 28.9k

• 5,164
1 vote

### Correctness of Solution for Forming a Committee with More Democrats than Republicans

To elaborate on the discussion in the comments: The given method is flawed as it multiply counts any committee that has more than the minimal number of Democrats. To avoid that, we split into even and ...
• 70.5k
1 vote

### combinations problem - teachers to groups

This is a bizarre sentence to read! I tried Benjamin Dickman's formula but it did not work out =, the right answer is 15504 I don't even know where to start. I will guess that you are referring to ...
• 14.5k

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