How many 7 different digit numbers can you create using all of the digits in the number 5,444,422?

Question

More textbook questions that i am still having a lot of trouble understanding, really need an answers really fast thank you very much.

Answer 1

If all the numbers were different, the total number of different numbers would be

DiffNum = 7! = 5040.

 

However, we have 5 - one digit, 4 - four digits and 2 - 2 digits.

 

DiffNum = 7!/(2! x 4!)

             = 5040 /48

             =105.

 

There are 105 different numbers we can write using the digits of 5,444,422.