Question

A family of 6 members that is made up of Papa, Mama and their 4 children go to the stadium to watch the Peru playoff game. They find 6 available seats together in the same row. How many ways can they be located if parents have to stay to the ends?

Answer 1

I believe the equation for formulas is

n!/(r!•(n-r)!)

n will be the total number of items, in this case, 6. r is the number of items being chosen, in this case, 4.

n! in this case will be:
6 • (6-1) • (6-2) • (6-3) • (6-4) • (6-5) = 6 • 5 • 4 • 3 • 2 • 1 = 720

r! will be:
4 • (4-1) • (4-2) • (4-3) = 4 • 3 • 2 • 1 = 24

Now to get (n-r)!
(n-r) = 2
(n-r)! = 2 • (2-1) = 2 • 1 = 2

So now we have:
720/(24 • 2) = 720/48 = 15

Then you would multiply by 2 because the parents each have two spots can sit in (the ones on the end) so the answer is 30.

I hope this helps.