Question

If a $5$ digits number is formed using only digits $0,1,3,4,4$, then the correct statements(s) is/are

• A. Total possible numbers are $48$
• B. Total possible numbers starting from $1$ are $12$
• C. the position of the number ${}^{\prime \prime }{41034}^{\prime }$, when arranged in increasing order is $32$
• D. the position of the number ${}^{\prime \prime }{34104}^{\prime \prime \prime }$, when arranged in increasing order is $21$

Answer 1

Answer: (A), (B), (D)

the position of the number ${}^{\prime \prime }{34104}^{\prime \prime \prime }$, when arranged in increasing order is $21$

Total numbers starting from $1$ are $\frac{4!}{2!}=12$
Total numbers starting from $3$ are $\frac{4!}{2!}=12$
Total numbers starting from $4$ are $4!=24$
Total possible numbers are $12+12+24=48$

Total numbers starting from $40$ are $3!=6$
Next number will be ${}^{\prime \prime }{41034}^{\prime \prime }$
The position of the number ${}^{\prime \prime }{41034}^{\prime \prime }$ is $=12+12+6+1=31$

Total numbers starting from $30$ are $\frac{3!}{2!}=3$
Total numbers starting from $31$ are $\frac{3!}{2!}=3$
Total numbers starting from $340$ are $2!=2$
Next number will be ${}^{\prime \prime }{34104}^{\prime \prime }$
The position of the number ${}^{\prime \prime }{34104}^{\prime \prime }$ is $=12+3+3+2+1=21$