Problem Solving

The president of a country and 4 other dignitaries are scheduled to sit in a row on 5 chairs. 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

What is the fastest way to solve this question. Would 5*5 - 1 (the president, who must sit in the center chair) always work? The Answer would be [spoiler](D)[/spoiler].

The position of the president is fixed. So remaining 4 people and 4 chairs is 4! ways = 24

I say Ashwin is right. Since you have got 4 sets left, only 4! is the answer you should have.

Xeb wrote:The president of a country and 4 other dignitaries are scheduled to sit in a row on 5 chairs. 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

What is the fastest way to solve this question. Would 5*5 - 1 (the president, who must sit in the center chair) always work? The Answer would be [spoiler](D)[/spoiler].

Xeb,


24 is right, but 5*5-1 is not a legitimate way to get there.

Think about the case where there are 2 dignitaries and 1 president with the same restriction of the president having to sit in the middle. If we represent the dignitaries by A and B, the possible orders are APB and BPA. Only two ways. Whereas your method would give 3*3-1=8.

Yes the perfect way would be 4 chairs 4 people * 1 chair 1 people
=> 4! * 1! = 24.