Question

All the numbers that can be formed using the digits of $12345$ are arranged in the decreasing order of magnitude. The rank of $32415$ is:

• A. $64$
• B. $62$
• C. $96$
• D. $128$

Answer 1

The correct option is A $64$

We should form $5$ digit number using digits $1,2,3,4,5$ and we have to find the rank of number $32415$

If the first digit is $1$ , then the number of possible numbers is $4\times 3\times 2\times 1=24$

If the first digit is $2$ , then the number of possible numbers is $4\times 3\times 2\times 1=24$

If the first digit is $3$ and second digit is $1$ , the number of possible numbers is $3\times 2\times 1=6$

If the first digit is $3$ , second digit is $2$ and the third digit is $1$ , the number of possible numbers is $2\times 1=2$

If the first digit is $3$ , second digit is $2$ and the third digit is $2$ , the number of possible numbers is $2\times 1=2$

If the first digit is $3$ , second digit is $2$ and the third digit is $3$ , the number of possible numbers is $2\times 1=2$

Therefore the rank of number $32415$ is $24+24+6+2+2+2+4=64$

So the correct option is $A$