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 ___________.

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Aicharya · Accepted Answer

We have, $5$ red, $4$ black, $3$ white marbles. Required number of ways $\begin{aligned} &= \binom{5}{0} 	imes \binom{7}{4} + \binom{5}{1} 	imes \binom{7}{3} + \binom{5}{2} 	imes \binom{7}{2} + \binom{5}{3} 	imes \binom{7}{1} \ &= 35 + 175 + 210 + 70 \ &= 490 \end{aligned}$

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then, the number of ways in which 4…

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