Permutations and Combinations 2 Question 21
21. A box contains two white balls, three black balls and four 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?
(1986, $2 \frac{1}{2}$ M)
Show Answer
Answer:
Correct Answer: 21. (64)
Solution:
- Case I When one black and two others balls are drawn.
$\Rightarrow \quad$ Number of ways $={ }^{3} C _1 \cdot{ }^{6} C _2=45$
Case II When two black and one other balls are drawn $\Rightarrow \quad$ Number of ways $={ }^{3} C _2 \cdot{ }^{6} C _1=18$ Case III When all three black balls are drawn
$\Rightarrow \quad$ Number of ways $={ }^{3} C _3=1$
$\therefore \quad$ Total number of ways $=45+18+1=64$
