Problem Solving

10. The president of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?
(A) 4
(B) 5
(C) 20
(D) 24
(E) 120




Hi,
I thought the answer was E) by doing 5P4 but the answer is D) ... Can you help?

Fix the president in the middle chair

Other 4 people can be arranged in 4*3*2*1 = 24 ways

hey there...can someone help? so in the case above you used 4! or n!, right? isn't n! when you must choose from a set of n objects from the source to fill specific spots when order matters?

so when would you use n!/(n-r)! ?

thx!

I believe the permutation formula you refer to still holds in this case. We have four spots to fill and four people to fill them, so

nPr = n!/(n-r)!

4P4 = 4!/(4-4)! = 4!/0! = 4! = 24

since 0! is defined to be 1.

Whenever there’s a question that involves that two people must sit together, or one person has to sit somewhere specifically, treat it as one person. Thus five becomes four factorial.

If all five people can sit anyway they want, then 5!