# A box contain 10 red marbles,20 blue marbles and 30 green marbles.5 marbles are drawn from the box.What is the probability that all will be blue?

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

Toolbox:
• $nC_r=\large\frac{n!}{r!(n-r)!}$
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.