Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?
(A) 9
(B) 12
(C) 15
(D) 36
(E) 720
Answer: D
Source: Official guide
Team A and Team B are competing against each other in a game of tug-of-war.
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Take the task of lining up the 6 competitors and break it into stages.BTGModeratorVI wrote: ↑Sat Aug 08, 2020 7:06 amTeam A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?
(A) 9
(B) 12
(C) 15
(D) 36
(E) 720
Answer: D
Source: Official guide
Stage 1: Select a competitor for the 1st position
This person must be a male.
Since there are 3 males to choose from, we can complete stage 1 in 3 ways
Stage 2: Select a competitor for the 2nd position
This person must be a female.
Since there are 3 females to choose from, we can complete stage 2 in 3 ways
Stage 3: Select a competitor for the 3rd position
This person must be a male.
There are 2 males remaining to choose from (since we already selected a male in stage 1), so we can complete stage 3 in 2 ways
Stage 4: Select a competitor for the 4th position
This person must be a female.
There are 2 females remaining to choose from. So we can complete stage 4 in 2 ways
Stage 5: Select a male for the 5th position
There's only 1 male remaining. So we can complete stage 5 in 1 way
Stage 6: Select a female for the 6th position
There's only 1 female remaining. So we can complete stage 6 in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus create a 6-person lineup) in (3)(3)(2)(2)(1)(1) ways (= 36 ways)
Answer: [D
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Solution:BTGModeratorVI wrote: ↑Sat Aug 08, 2020 7:06 amTeam A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?
(A) 9
(B) 12
(C) 15
(D) 36
(E) 720
Answer: D
Source: Official guide
We need to determine the number of ways to lineup male, female, male, female, male, female.
Since there are 3 males, we have 3 options for the first spot, and since there are 3 females, we have 3 options for the second spot. Then we have 2 options for the third spot, 2 options for the fourth, and 1 option for each of the last two spots. Thus, the number of ways to lineup that group is 3 x 3 x 2 x 2 x 1 x 1 = 36.
Answer: D
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