Question

From 80 cards numbered 1 to 80, two cards are drawn at random. The probability that the cards have the numbers divisible by 4 is

• A. $\frac{15}{316}$
• B. $\frac{17}{316}$
• C. $\frac{19}{316}$
• D. $\frac{21}{316}$

Answer 1

The correct option is C $\frac{19}{316}$

we can see there are $20$ numbers between $1$ to $80$, which are divisible by $4$, so number of ways of choosing $2$ cards divisible by $4$ is ${}^{20}{C}_2$. Similarly, total number of ways of choosing $2$ cards out of $80$ cards is ${}^{80}{C}_2$.
Thus, Probability $=\frac{{}^{20}{C}_2}{{}^{80}{C}_2}=19/316$