Four numbers are multiplied together. Then the probability that the product will be divisible by 5 or 10 is a. `369/625` b. `399/625` c. `123/625` d. none of these

Options

A. `(369)/(625)`
B. `(399)/(625)`
C. `(123)/(625)`
D. `(133)/(625)`

Answer

A

Explanation

The divisibility of the product of four numbers depends upon the value of the last digit of each number. The last digit of a number can be any one of the ten digits 0,1,2,..,9. So, the total number of ways of selecting last digits of four numbers is `10xx10xx100xx10=10^(4)`. If the product of the 4 numbers is not divisible by 5 or 10, then the number of choices for the last digit of each number is 8 (excluding 0 or 5).
So, favourable number of ways `=8^(4)`.
Therefore, the probability that the product is not divisible by 5 or 10 is `(8//10)^(4)`
Hence, required probability `=1-((8)/(10))^(4)=(369)/(625)`