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 $\frac{10}{21}$

Assuming that the question is to find probability of getting exactly 2 defective systems.
Number of ways in which $5$ items can be selected
= ${}^{10}{C}_5=252$
Number of ways in which $2$ defective systems and $3$ non-defective systems can be selected
= ${}^4{C}_2\times {}^6{C}_3=6\times 20=120$
Required probability=$\frac{120}{252}$=$\frac{10}{21}$