A box contains 6 white balls and 5 red balls. in how many ways 4 balls can be drawn from the box if

1. They are to be any color

2. All the balls to be of same color.

Solution:

Total balls = 6+5 = 11

Total number of balls in a box is 11.

No of balls drawn is 4.

1] 4 balls of any color = $11C_4 = \frac{11.10.9.8}{1.2.3.4} = 330$

4 balls drawn from the box of any color is 330 balls.

2] All balls to be of same color.

$6c_4 + 5c_4 = \frac{6.5.4.3}{1.2.3.4} + \frac{5.4.3.2}{1.2.3.4}$

= 15 + 15

= 20 balls.

$\therefore$ All the balls drawn of same color is 20.

Box 6 white 5 Red