First slide

Combinations

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 _

Moderate

Solution

$\begin{array}{l} \begin{array}{l} 0 Red, & 1Red, & 2Red, & 3Red \end{array} \\ Numebr of ways {}^{7}C_{4} + {}^{5}C_{1} \cdot {}^{7}C_{3} + {}^{5}C_{2} \cdot {}^{7}C_{2} + {}^{5}C_{3} {}^{7}C_{1} = 35 + 175 + 210 + 70 = 490 \end{array}$

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