Each student has exactly a 92% chance of passing the final exam. What is the probability that exactly 5% of 140 students fail the exam​

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$$\begin{gathered} \mathrm{Probabiltiy} \mathrm{of} \mathrm{passing} \mathrm{the} \mathrm{exam}=\mathrm{x}=92\%=\frac{92}{100}=\frac{23}{25} \\ \mathrm{Probabilty} \mathrm{of} \mathrm{failing} \mathrm{the} \mathrm{exam}=\mathrm{y}=1-\frac{23}{25}=\frac{2}{25} \\ 5\% \mathrm{of} 140=\frac{5}{100}\times 140=7 \\ \mathrm{So} \mathrm{we} \mathrm{want} 7 \mathrm{students} \mathrm{to} \mathrm{fail} \mathrm{so} \mathrm{we} \mathrm{will} \mathrm{select} 7 \mathrm{students} \mathrm{out} \mathrm{of} 140 \mathrm{and} \\ \mathrm{assign} \mathrm{them} \mathrm{probabilty} \mathrm{of} \mathrm{failing} \mathrm{the} \mathrm{exam} \mathrm{and} \mathrm{while} \mathrm{assigning} \mathrm{probabilty} \\ \mathrm{of} \mathrm{passing} \mathrm{to} \mathrm{remaining} \mathrm{students}. \mathrm{Hence} \mathrm{required} \mathrm{probabilty} \\ \mathrm{Required} \mathrm{Probabilty}{=}^{140}{\mathrm{C}}_7 {\left(\frac{2}{25}\right)}^7 {\left(\frac{23}{25}\right)}^{140-7} \\ \mathbf{\Rightarrow }\mathbf{Required}\mathbf{ }\mathbf{Probabilty}{\mathbf{=}}^{\mathbf{140}}{\mathbf{C}}_{\mathbf{7}}\mathbf{ }{\left(\frac{\mathbf{2}}{\mathbf{25}}\right)}^{\mathbf{7}}\mathbf{ }{\left(\frac{\mathbf{23}}{\mathbf{25}}\right)}^{\mathbf{133}} \end{gathered}$$

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