Question

Five different digits from the set of numbers $\{1,2,3,4,5,6,7\}$ are written in random order. How many numbers can be formed using $5$ different digits from set $\{1,2,3,4,5,6,7\}$ if the number is divisible by $9$?

• A. $\frac{127}{283}$
• B. $\frac{21}{726}$
• C. $\frac{162}{389}$
• D. $\frac{120}{726}$

Answer 1

The correct option is D $\frac{120}{726}$

Given the digits=$1,2,3,4,5,7$

No. of $5$digit no. that can be formed without repetition and without taking into considering any restrictions is$5!$ is $120$.

For a no. to be divisible by$9$, the units place must contain a no. which is a multiple of $9$.

So, in this case the units place can be filled in$2$ways by $3$and$6$ .i.e, $3!+6!=726$ ways

$\therefore$ The required probability $=\frac{120}{726}$