How many differen

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Four letters E, KRD Sharma - Mathematics

. There are 6 iteRD Sharma - Mathematics

How many permutatRD Sharma - Mathematics

Find the total nuRD Sharma - Mathematics

In how many ways RD Sharma - Mathematics

From among the 36RD Sharma - Mathematics

How many differenRD Sharma - Mathematics

How many three-diRD Sharma - Mathematics

In how many ways RD Sharma - Mathematics

How many three-diRD Sharma - Mathematics