Question

How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.

Answer 1

Numbers greater than 50000 can either have 5 or 9 in the first place and will consist of 5 digits.
Number of arrangements having 5 as the first digit = $\frac{4!}{2!}$

Number of arrangement having 9 as the first digit = $\frac{4!}{2!}$
∴ Required arrangements = $\frac{4!}{2!}$+$\frac{4!}{2!}$ = 24