Question

A nine-digit number is formed using the digits $1,2,3,5$ and $7$ . The probability that the product of all digits is always $1920$ is

• A. $\frac{1}{5^{9}}$
• B. $\frac{7}{5^{8}}$
• C. $\frac{72}{5^{9}}$
• D. $\frac{1}{7 !}$

Answer 1

Answer: (C)

Total cases $=5^{9}$
$1920=5\times 3\times 2^{7}$
Favourable cases = no. of ways of arrangement of $5,3,2,2,2,2,2,2,2$ in a row $=\frac{9 !}{7 !}$
hence, required probability $=\frac{72}{5^{9}}$