# Tagged Questions

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### The physical meaning of ${n \choose k} = {n \choose n-k}$.

They say that $${n \choose k}={n \choose n-k}.$$ Can someone explain its physical meaning? Among many problems that use this proof, here is an example: The english alphabet has $26$ letters ...
1answer
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1answer
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### Multiple choice questions on relations and some of their properties

I'm confused about these 3 selected problems. I have the solutions for each, if necessary, but I'm much more interested in understanding the material. If anyone can offer a clear, concise, and ...
1answer
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### Upcoming exam! Any good sources to learn about counting techniques and discrete probability?

If anyone has a free, online source to contribute for a certain topic/topics, please share! I'm not really looking for an intense theoretical grasp of these topics, just an intuitive understanding of ...
3answers
720 views

### Trouble understanding equivalence relations and equivalence classes…anyone care to explain?

What exactly are equivalence relations and equivalence classes? The latter is giving me the most trouble; I've tried to read multiple sources online but it just keeps going over my head. Example ...
1answer
105 views

### Suppose you flip a weighted coin…

Suppose you flip a weighted coin that is $3$ times more likely to come up heads. What is the probability that, if you flip the coin $3$ times, you will get an even number of heads? Can someone help ...
1answer
771 views

### How many strings of six lowercase letters contain the letters a and b in consecutive positions…

How many strings of six lowercase letters contain the letters a and b in consecutive positions with a preceding b, with all letters distinct? Can someone give me a general method for thinking about ...
1answer
145 views

### Intuition about the relation of combinations and entropy

It is not difficult to show that $${n \choose \lambda n} \leq 2^{H(\lambda)n}$$ where $H$ is the binary entropy function: $$H(\alpha) = -\alpha \lg \alpha - (1-\alpha)\lg (1-\alpha)$$ I was ...
3answers
141 views

### Seemingly similar but different probability games

Burger King is currently running its "family food" game in which each piece can be modeled as a scratch off game where exactly one of three slots is a winner and you may only scratch one slot as your ...
0answers
173 views

### Ways to think about the binomial coefficient

Just to sharpen my intuition in combinatorics, I ask you of ways to think about interesting combinatorical quantities and expressions like the binomial coefficient, for example, for the binomial ...
2answers
1k views