From a group of 18 athletes that include 10 people with professional experience, a 3-person team is to be selected so that exactly 1 person on the team has professional experience. How many different teams of this type are possible?
(A) 280
(B) 360
(C) 504
(D) 560
(E) 816
![]()
(A) 280
(B) 360
(C) 504
(D) 560
(E) 816
Spoiler: ::
Explanation:
The team were looking for will choose 1 person from a population of 10 with professional experience. There are 10 such choices. The team will also have 2 people from the remaining 8 who do not have professional experience. The number of such choices is determined by the combinations formula: n!/k!(nk)! = 8!/2!(82)! = 8!/2!6! = 87/2 = 28
Since there are 10 choices for the one professional and 28 choices for the pairs of non-professionals, the total number of possible teams is the product: 28 10 = 280, choice (A).
The team were looking for will choose 1 person from a population of 10 with professional experience. There are 10 such choices. The team will also have 2 people from the remaining 8 who do not have professional experience. The number of such choices is determined by the combinations formula: n!/k!(nk)! = 8!/2!(82)! = 8!/2!6! = 87/2 = 28
Since there are 10 choices for the one professional and 28 choices for the pairs of non-professionals, the total number of possible teams is the product: 28 10 = 280, choice (A).