Question

The number of five digit numbers formed using the digits $0,2,2,4,4,5$ which are greater than $40,000$ is

• A. 84
• B. 90
• C. 72
• D. 60

Answer 1

Answer: (B)

90

All the numbers should start with $4$.
Hence keeping it fixed, we get
$=\frac{5!}{2!}$ numbers. ...(i)
Similarly for numbers starting with $5$
$=\frac{5!}{2!2!}$ ...(ii)
Hence, total numbers are $\frac{5!}{2!}+\frac{5!}{2!2!}$
$=60+30$
$=90$