$\begin{array}{1 1}(A)\;\large\frac{20C_5}{60C_5}\\(B)\;\large\frac{19C_5}{29C_5}\\(C)\;\large\frac{39C_5}{29C_5}\\(D)\;\large\frac{10C_5}{20C_5}\end{array} $

- $nC_r=\large\frac{n!}{r!(n-r)!}$

Step 1:

10 Red marbles

20 Blue marbles

30 Blue marbles

5 marbles are drawn at random

$\therefore$ Total number of ways selecting 5 marbles out of 60 marbles=$60C_5$

Step 2:

All will be blue.

Let E be the event,all marbles will be blue.

$\therefore n(E)=20C_5$

$\therefore$ Required probability =$\large\frac{n(E)}{n(S)}$

$\Rightarrow \large\frac{20C_5}{60C_5}$

Hence (A) is the correct answer.

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