A box contains $10$ 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?
A box contains $10$ 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?
Total number of marbles $=10+20+30=60$
Number of ways of drawing $5$ marbles from $60$ marbles $=^{60} C_{5}$
All the drawn marbles will be blue if we draw $5$ marbles out of $20$ blue marbles.
$5$ blue marbles can be drawn from $20$ blue marbles in $^{20} C_{5}$ ways.
$\therefore$ Probability that all marbles will be blue $\frac{{^{20}{C_5}}}{{^{60}{C_5}}}$
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