Question

Among the divisors of $504$, two distinct divisors are chosen randomly. The probability such that both the divisors chosen are even is -

• A. $\frac{51}{92}$
• B. $\frac{3}{4}$
• C. $\frac{9}{16}$
• D. $\frac{1}{12}$

Answer 1

Answer: (A)

$\frac{51}{92}$

$504=2^3\times 3^2\times 7$
So, the factors are $4\times 3\times 2=24$.
The number of even factors will be $3\times 3\times 2=18$.
If we randomly choose any two factors out of total $24$, then the total number of ways of doing it is ${}^{24}{C}_2$
Similarly, the number of ways of choosing two even factors is equal to ${=}^{18}{C}_2$.
Hence, the required probability $=\frac{{}^{18}{C}_2}{{}^{24}{C}_2}=\frac{18\times 17}{24\times 23}=\frac{51}{92}$