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  4. A box contains 6 red, 5 blue and 4 white marbles. Four marbles are chosen at random without replacement. The probability that there is atleast one marble of each colour among the four chosen, is

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Q. A box contains 6 red, 5 blue and 4 white marbles. Four marbles are chosen at random without replacement. The probability that there is atleast one marble of each colour among the four chosen, is

Probability - Part 2

Solution:

$P(E) = P(R R B W$ or $B B R W$ or $W W R B)$
image
$n ( E )={ }^6 C _2 \cdot{ }^5 C _1 \cdot{ }^4 C _1+{ }^5 C _2 \cdot{ }^6 C _1 \cdot{ }^4 C _1+{ }^4 C _2 \cdot{ }^6 C _1 \cdot{ }^5 C _1 $
$n ( S )={ }^{15} C _4$
$\therefore P ( E )=\frac{720 \cdot 4 !}{15 \cdot 14 \cdot 13 \cdot 12}=\frac{48}{91} $