Question

A box contains 2 white, 3 black and 5 red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?
a.29
b.36
c.48
d.85

Answer 1

Given:

Number of white balls in the box = 2

Number of black balls in the box = 3

Number of red balls in the boc = 5

To find:

Number of ways in which 3 balls can be drawn from the box if at least one black ball is to be included in the draw.

Solution:

If at least one black ball is to be included in the draw then there woule 3 possibilities:

1. Exactly one black and 2 non-black balls = 3C1 × 7C2
2. Exactly 2 black and 1 non-black balls = 3C2 × 7C1
3. Exactly 3 black and 0 non-black balls = 3C3 × 7C0

Hence the total number of possibilities will be:

3C1 × 7C2 + 3C2 × 7C1 + 3C3 × 7C0

= 85

Thus the correct option is D i.e. 85.