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

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) (1/59) (B) (7/58) (C) (72/59) (D) (1/7 !)

Tardigrade Admin · Accepted Answer

Total cases =59 1920=5× 3× 27 Favourable cases = no. of ways of arrangement of 5,3,2,2,2,2,2,2,2 in a row =(9 !/7 !) hence, required probability =(72/59)

Q. 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

$\frac{1}{5 ^{9}}$

$\frac{7}{5 ^{8}}$

$\frac{72}{5 ^{9}}$

$\frac{1}{7 !}$

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 $= \frac{72}{5 ^{9}}$

Q. 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

591​

587​

5972​

7!1​