On an average, rain falls on 12 days in every 30 days, find the probability that, rain will fall on just 3 days of a given week.

On an average, rain falls on 12 days in every 30 days

$p=\frac{12}{30}=\frac{2}{5};q=1-p=1-\frac{2}{5}=\frac{3}{5}\Rightarrow n=7\text{ and }r=3$

$p(x=r){=}^n{C}_r{p}^r{q}^{n-r}\Rightarrow p(x=3){=}^n{C}_3{p}^3{q}^{n-3}$

${=}^7{C}_3{\left(\frac{2}{5}\right)}^3{\left(\frac{3}{5}\right)}^4=\frac{35\times 2^3\cdot 3^4}{5^7}$