Question

Three distinct digits are selected from the set $\{1,2,3,4,5,6,7,8,9\}$ and then the three digits are multiplied together to form a number $N$. The chance that $N$ is a multiple of 10 is

• A. $\frac{2}{7}$
• B. $\frac{2}{21}$
• C. $\frac{7}{21}$
• D. $\frac{11}{42}$

Answer 1

Answer: (D)

Let $E$ : event that $N$ is a multiple of 10
$P ( E )= P$ (out of 3 digits, 5 is one of the digit and atleast one other is even)
$=\frac{{ }^4 C _2+{ }^4 C _1 \cdot{ }^4 C _1}{{ }^9 C _3}=\frac{6+16}{84}=\frac{22}{84}=\frac{11}{42}$