Question

There are $4$ defective items in a lot consisting of $10$ items. From this lot we select $5$ items at random. The probability that there will be $2$ defective items among them is?

• A. $\frac{1}{2}$
• B. $\frac{2}{5}$
• C. $\frac{5}{21}$
• D. $\frac{10}{21}$

Answer 1

The correct option is D $\frac{10}{21}$

number of defective items $=4$

Total number of items $=10$

number of ways to select $5$ items $={{}^{10}C}_5=\frac{10!}{5!(10-5)!}=252$

number of ways in which $2$ defective systems and $3$ non defective are selected

${{}^{4}C}_2\times {{}^{6}C}_3=6\times 20=120$

probability $=\frac{120}{252}=\frac{10}{21}$