Mathematics - Probability Question with Solution | TestHub

$n(S)=$ Total number of ways $=1000$ The favourable cases that the sum of the digits of the marked number on the page is equal to 9 are one digit number or two digits numbers or three digits numbers, if three digit number is $abc$. Then, $a+b+c=9;0\le a,b,c\le 9$. $\therefore n(E)=$ Number of favourable ways $=$ Number of solutions of the equation $={}^{9+3-1}{C}_{3-1}={}^{11}{C}_2=55$ $\therefore$ Required probability $=\frac{n(E)}{n(S)}=\frac{55}{1000}=\frac{11}{200}$.