Question

Illustration 6.36 Five different digits from the set of numbrs {1,2,3,4,5,6,7} are written in random order. How many nuber can be formed using 5 different digits from set {1,2,3,4,5,6,7} if the number is divisible by 9 ?

Answer 1

We have,

Five different digits from the set of numbers $\{1,2,3,4,5,6,7\}$ are written in random order.

Then An integer is divisible by $9$ if the sum of digits is divisible by $9$

Since, the sum of first natural number is $\frac{9(9+1)}{2}=45$, which is divisible by 9.

We don’t pick to from the five digit number is divisible by 9.

Then the number of ways of choosing two integers from 9 integers

$\{(1,4),(2,7),(3,6),(4,5)\}=4$

The, ratio to get probability that the five digit number so formed is divisible by $9$.

Then,

$\frac{4}{36}=\frac{1}{9}$

Hence, this is the answer.