Question

The coughlin family discovered they can stand in a row for their family portrait in 720 diferent ways. How many members are in the coughlin family

Answer 1

There are six (6) members of the family.

The first person in the row can be any 1 of the 6.  For each choice . . .
The 2nd person in the row can be any 1 of the other 5.  For each choice . . .
The 3rd person in the row can be any 1 of the other 4.  For each choice . . .
The 4th person in the row can be any 1 of the other 3.  For each choice . . .
The 5th person in the row can be any 1 of the other 2.  For each choice . . .
The 6th person in the row is the 1 who is left.

Total number of ways to line up = (6 x 5 x 4 x 3 x 2 x 1) = 720 ways .

This number is called " six factorial ", and it's written ' 6! ' .