MathProblemSolver101

I remember this from this years AMC 10 lol

1/a + 1/b = 1/3

2/a + 1/b = 1/2

$\binom{4}{1, 2, 3, 4}$

Hi,

I think that is the mean, not median 

Principle of inclusion exclusion

X/2 + x/3 + x/6 = 180

3x + 2x +x =180 * 6

6x = 180*6

x = 180
 

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4c3 = 4c1= 4

-mps101

$(3p+1)(t-4)=2tp$

$3tp - 12p + t - 4 = 2tp$

$tp - 12p + t - 4 = 0$

$t(p+1) = 12p + 4$

$t(p+1) = 4(3p + 1)$

$t = 4 \left(\frac{3p+1}{p+1}\right)$

$t = 4 \left(\frac{3p + 3 - 2}{p+1}\right)$

$t = 4 \left(3 - \frac{2}{p+1}\right)$

$t \leq 24$

Continue with https://web2.0calc.com/questions/the-powers-of-coffee-in-mathematicians#r2

You have: $(1, 3, 4, 5, 5, 6), (1, 2, 2, 3, 4, 5, 6)$

For $1,$ you can only have $6,$ and there is $1$ of them, so $1$ way to do this.

For $3,$ you can only have $4,$ and there is $1$ of them, so $1$ way to do this.

For $4,$ you can only have $3,$ and there is $1$ of them, so $1$ way to do this.

For both of the $5,$ you can only have $2,$ and there are $2$ of them, so $2 \times 2 = 4$ way to do this.

For $6,$ you can only have $1,$ and there is $1$ of them, so $1$ way to do this.

In total, there are $1 + 1 + 1 + 4 + 1 = \boxed{8}$