Question

The number of numbers greater than $50,000$ that can be formed by using the digits $3,5,6,6,7,9$ is

• A. $47$
• B. $48$
• C. $50$
• D. none of these

Answer 1

The correct option is B $48$

Since any number greater than $50,000$ contains $5$ digits, we have to take all the $5$ digits out of which the digit $6$ is repeated twice.

So number of permutations is $\frac{5!}{2!}=60$

But out of these arrangements we have to reject those which begin with $3$ as in that case, the numbers will be less than $50000$.

We find all such numbers by fixing 3 at extreme left. So remaining 4 digits can be filled in $\frac{4!}{2!}=12$

Required number of number is $60-12=48$