Question:
An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is_________.
Solution:
0 Red, 1 Red, 2 Red, 3 Red
Number of ways of selecting atmost three red balls
$={ }^{7} C_{4}+{ }^{5} C_{1} \cdot{ }^{7} C_{3}+{ }^{5} C_{2} \cdot{ }^{7} C_{2}+{ }^{5} C_{3} \cdot{ }^{7} C_{1}$
$=35+175+210+70=490$
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