Question

All the five digit numbers that can be formed using the digits $1,2,3,4,5$, without repetition, are arranged in the decreasing order of magnitude. The rank of the number $34215$ is

• A. $58$
• B. $62$
• C. $96$
• D. $128$

Answer 1

The correct option is A $58$

Numbers with the leftmost digit $5$ are $4!=24$
Similarly, numbers with the leftmost digit $4$ are $4!=24$
If a $5$ digit number starts with $3$, the cases where the digit next to $3$ is $5$ is equal to $3!=6$
Next, if the numbers starting with $34$ are arranged in decreasing order we will get the following numbers in order:

$34521,34512,34251,34215$

Hence, the rank of $34215$ is $24+24+6+4=58$