Finding the number of possibilities

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Homework Statement



A stockbroker purchases 5 different stocks. During the next month, each stock can either raise,fall or stay the same. How many different possibilities are there?

Homework Equations





The Attempt at a Solution


For each stock, there are 3 possible choices(raise,fall,same). For each of the choices, there are 4 possible outcomes. From that, i multiplied 5*3*4*4*4=960 but it's wrong. Anyone know where i went wrong with my reasoning?
 
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nvm i found the answer lol
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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