Question

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? [Official GMAT-2018]

Hint:

When arranging a set of items with restrictions, use factorials to calculate the number of permutations for each set and multiply the results.

Answer 1

Step 1: Understand the arrangement for Team A.
Team A has 3 males and 3 females. The lineup needs to alternate between males and females. Thus, the order will be: male, female, male, female, male, female.
Step 2: Calculate the number of ways to arrange the males and females.
- The 3 males can be arranged in 3! ways.
- The 3 females can also be arranged in 3! ways.
Step 3: Calculate the total number of lineups.
The total number of possible lineups is the product of the arrangements of males and females: \[ \text{Total lineups} = 3! \times 3! = 6 \times 6 = 36 \] Step 4: Conclusion.
The total number of possible lineups is 36.