Question

A box contains $2$ white, $3$ black and $4$ red balls.(Balls are of different sizes). In how many ways can $3$ balls be drawn from the box if atleast one black ball is to be included in the draw?

• A. $84$
• B. $64$
• C. $60$
• D. $120$

Answer 1

The correct option is B $64$

We have $2$ white, $3$ black and $5$ red balls.

So in total we have $10$ balls, out of which we can draw only $3$ balls.

We have to draw at least one black ball, so three conditions arises 1 black, 2 black and 3 black

$\therefore$Total number of ways

${=}^6{C}_2{.}^3{C}_1{+}^6{C}_1{.}^3{C}_2{+}^6{C}_0{.}^3{C}_3$

$=64$