Question

How many different numbers, greater than 50000 can be formed with the digits $ 0,1,2,5,9 $ .

Answer 1

Hint: We first find the condition which defines the numbers to be greater than 50000 formed with the digits $ 0,1,2,5,9 $ . We find the number of choices for the places to fill up and then find the multiplication of those numbers.

Complete step by step solution:
We find numbers greater than 50000 formed with the digits $ 0,1,2,5,9 $ only when the starting digit of the number is 5 or 9.
So, the condition to make such numbers is to keep 5 or 9 as the starting number.
Permutation of the rest of the digits can be done for the numbers.
Therefore, for the first position of the number we have 2 options. We are left with 4 digits and 4 places to cover.
The number of choices for filling up the places will be $ 4!=24 $ .
Therefore, the total number of unique numbers will be $ 2\times 24=48 $ .
So, the correct answer is “48”.

Note: We need to remember that if the number starts with 0 then the number changes to 4-digit number from 5-digit number. But with the condition of keeping 5 or 9 as the starting number omits the possibility of 0 being the starting number.