There are 27 students on the college debate team what 's the pobability

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Homework Statement



there are 27 students on the college debate team what 's the pobability that at least 5 of them have their birthday in the same month??


Homework Equations





The Attempt at a Solution

 
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Please show2. Homework Equations
3. The Attempt at a Solution
 
Sum from x=5 to x=27 of
Choose(27,x)*(1/12)x*(11/12)27-x

Can anybody confirm?
 

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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