what is the difference between ${10 \choose 2}$ and ${10 \choose 1}\times{9 \choose 1}$?
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what is the difference between ${10 \choose 2}$ and ${10 \choose 1}\times{9 \choose 1}$?

I'm not able to understand the difference between these two. Don't both just give the number of ways of selecting $2$ objects from a total of $1...

Published: Aug 30, 2026

How do I compute a double weighted average? In other words, an average with two weighting factors.
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How do I compute a double weighted average? In other words, an average with two weighting factors.

This might be a simple question... I was wondering, how does one take a double weighted average? (honestly, don't know if that is what it is called)....

Published: Aug 30, 2026

Expected number of coin flips to get three heads or three tails
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Expected number of coin flips to get three heads or three tails

We both play a game where we flip a coin. You win if 3 heads appear, I win if 3 tails appear. What is the expected number of flips for the game to end. Th...

Published: Aug 30, 2026

How are the known digits of $\pi$ guaranteed?
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How are the known digits of $\pi$ guaranteed?

When discussing with my son a few of the many methods to calculate the digits of $\pi$ (15 yo school level), I realized that the methods I know more or le...

Published: Aug 30, 2026

Proving a statement using the definition of a limit
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Proving a statement using the definition of a limit

Let $f$ be a function that is defined on a deleted neighbourhood of $x_0 ∈ \Bbb R$, such that $f(x) \ne 0$ for every $x$ on that deleted neighbourhood. Su...

Published: Aug 30, 2026

What is the measure of angle F?
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What is the measure of angle F?

This is an isosceles triangle with base angles being the only part filled in. I have trouble understanding that if the base angles are not like terms, the...

Published: Aug 30, 2026

Some tips on 3D Trig?
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Some tips on 3D Trig?

I understand this isn't a MATHS question specifically, however, sometimes I have trouble identifying when to use 3D trig, and trouble with it in gene...

Published: Aug 30, 2026

What is an indexed set?
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What is an indexed set?

I stuck on something. I am trying to understand what is said in the image I linked above. "A function I from a set Λ onto a set a is said to index the set...

Published: Aug 30, 2026

Question on the 'Hat check' problem
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Question on the 'Hat check' problem

The famous 'Hat Check Problem' goes like this, 'n' men enter the restaurant and put their hats at the reception. Each man gets a rando...

Published: Aug 30, 2026

Notation for elements of a vector
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Notation for elements of a vector

If I want $x_i$ to be an arbitrary element of a vector $\vec{x}$ can I use the following notation: $x_i \in \vec{x}=[x_1\;x_2\;\cdots\;x_n]^T\in R^n$ ? An...

Published: Aug 30, 2026

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