Question

How many eight-digit serial numbers contain three of one digit, two of another digit, two of yet another digit, and one of still another digit?

Answer 1

It is easier to understand the problem if you create a number based on the criteria and then perform the computations. I am going to choose: 111 22 33 4

There are 10 options for the first "1" and only 1 option for the other two 1's

There are 9 remaining options for the first "2" and only 1 option for the other 2

There are 8 remaining options for the first "3" and only 1 option for the other 3

There are 7 remaining options for the "4"

10 x 1 x 1    x      9 x 1     x      8 x 1      x      7

10 x 9 x 8 x 7 = 5,040

Answer: 5,040