A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

Question

Smart Achievers · Accepted Answer

(1)

$In order to draw 3 balls, six cases arise:$

$\begin{matrix} Case & Number of ways \\ 1 black, 1 white, 1 red & {}^{3}C_{1} \times {}^{2}C_{1} \times {}^{4}C_{1} = 24 \\ 1 black, 2 white, 0 red & {}^{3}C_{1} \times {}^{2}C_{2} \times {}^{4}C_{0} = 3 \\ 1 black, 0 white, 2 red & {}^{3}C_{1} \times {}^{2}C_{0} \times {}^{4}C_{2} = 18 \\ 2 black, 0 white, 1 red & {}^{3}C_{2} \times {}^{2}C_{0} \times {}^{4}C_{1} = 12 \\ 2 black, 1 white, 0 red & {}^{3}C_{2} \times {}^{2}C_{1} \times {}^{4}C_{0} = 6 \\ 3 black, 0 white, 0 red & {}^{3}C_{3} \times {}^{2}C_{0} \times {}^{4}C_{0} = 1 \end{matrix}$

$∴$ $Total number of ways = 64$

Solution

Q.
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw

1 64

2 24

3 3

4 12

Want Us to Email you About Special Offers & Updates?