Problem Solving

The Â…ve sides of a pentagon have lengths of 2, 3, 4, 5, and 6
inches. Two pentagons are considered di¤erent only when the
positions of the side lengths are di¤erent relative to each other.
What is the total number of di¤erent possible pentagons that
could be drawn using these Â…ve side lengths?
(A) 5
(B) 12
(C) 24
(D) 32
(E) 120

maihuna wrote:The Â…ve sides of a pentagon have lengths of 2, 3, 4, 5, and 6
inches. Two pentagons are considered di¤erent only when the
positions of the side lengths are di¤erent relative to each other.
What is the total number of di¤erent possible pentagons that
could be drawn using these Â…ve side lengths?
(A) 5
(B) 12
(C) 24
(D) 32
(E) 120

It is like a ring. So, required no. = (n-1)!/2 = (5-1)!/2 = 12 B
Please note that a ring is different from a circular table scenario in the sense that two arrangements for example 1-2-3-4 is same as 1-4-3-2(if you flip the ring) .[/spoiler]

one more for 12....same reason