Question

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

Answer 1

1, 1, 5, 9, 0. Five digits are, 2 alike and 3 different. Numbers greater than 50000 will have either 5 or 9 in the first place and will consist of 5 digits.
Let 5 be in the first place then we have to fill the remaining 4 places by remaining 4 digits 1, 1, 9, 0 out of which 2 are alike and hence it will be
$\frac{4!}{2!}=\frac{24}{2}=12$.
Similarly 12 is the number when 9 is in the first place.
Therefore total numbers are 12 + 12 = 24 which are greater than 50000.