# Quod Erat Demonstrandum

## 2015/01/23

### 某數算題

Filed under: mathematics,NSS — johnmayhk @ 5:34 下午
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Just reply to a F.5C student on a basic core mathematics question (on P.5.38):

There are 8 outstanding students from junior forms and 9 outstanding students from senior forms in a school this year. 5 out of these 17 students are now selected for an overseas exchange programme. Find the number of combinations of selecting at least 1 student from junior forms and 1 from senior forms.

Here is the ‘so-called’ solution from a student:

$_8C_1\times _9C_1\times _{15}C_3$

as the student claimed, select 1 from junior, $_8C_1$ ways; select 1 from senior, $_9C_1$ ways; then select the remaining 3 students from the remaining 15 students, $_{15}C_3$ ways, hence, the total number of combination should be $_8C_1\times _9C_1\times _{15}C_3$, right?

Sorry, it is incorrect. (more…)

## 2015/01/12

### just a core math question involving variance

Filed under: mathematics,NSS — johnmayhk @ 10:35 下午

Just reply to a student about a core math question used in school exam.

Question

Let $m$, $v$ be the mean and variance of {$2x_1, 2x_2, 2x_3$} respectively.

Show that the mean and variance of the set

{$x_1+x_1,x_1+x_2,x_1+x_3,x_2+x_1,x_2+x_2,x_2+x_3,x_3+x_1,x_3+x_2,x_3+x_3$}

are $m$ and $\frac{v}{2}$ respectively.

Proof

(Mean) For the original set, (more…)

## 2015/01/09

### 推特老題

Filed under: HKALE,Pure Mathematics — johnmayhk @ 3:26 下午
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１１
１２１
１３３１
１４６４１

## 2015/01/08

### 被 8 整除

Filed under: Fun,mathematics — johnmayhk @ 2:08 下午
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1.問題

$n^4+2n^3+3n^2+2n$

2.解答

(a)