ganand wrote:
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
Take the task of lining up the 6 competitors and break it into
stages.
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:
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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