Q. 114.3( 4 Votes )

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

Answer :

Given, the numbers 0, 1, 1, 5, 9. Total of 5 digits, and it has 1 repeated digit 1 repeated twice.

To find: Number of numbers that can be formed using digits 0, 1, 1, 5, 9 in such a way that arranged number is greater than 50000. Notice that an arrangement in which the first digit is either 5 or either 9 will only produce number greater than 50000. We have to find such numbers.


The problem can now be rephrased as to find a total number of permutations of 5 objects (0, 1, 1, 5, 9) of which two objects are of same type (1, 1), And all other objects are distinct. But, either 5 or 9 will be only in the first place (According to question).


First, we will find a total number of permutations of these 5 digits starting with 5 and then we will find the total number of permutations of these 5 digits starting with 9. Addition of these two numbers will give us the required numbers greater than 50000.


Total number of permutations starting with 5 will be equals to permutations of remaining digits (0, 1, 1, 9) in 4 remaining places


Total number of permutations starting with 9 will be equals to permutations of remaining digits (0, 1, 1, 5) in 4 remaining places


Number of permutations in which either 5 or 9 will come at first place will be equal to



= 24


Hence, total number of permutations of 5 digits (0, 1, 1, 5, 9) forming a 5 digit number greater than 50000 is equals to 24.


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