In how Many Different Ways Can a Group of 8 People be Divided into 4 Teams of 2 People Each?

Question: In how many different ways can a group of 8 people be divided into 4 teams of 2 people each?

1. 90
2. 105
3. 168
4. 420
5. 2520

“In how many different ways can a group of 8 people be divided into 4 teams of 2 people each?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

As written in question, we have 4 teams (total 8 people), each team having 2 people.

This can be written as: \(\frac{^8C_2*^6C_2*^4C_2*^2C_2}{4!}\)

After solving this equation, we get:

\(\frac{^8C_2*^6C_2*^4C_2*^2C_2}{4!}\)= 105

We have divided it by 4! because order of the teams does not matter.

Now as we have total 8 people forming 4 teams (2 people in each team), so the possible pairs that can be formed as:

People are: 1, 2, 3, 4, 5, 6, 7, and 8

Teams= (1, 2), (3, 4), (5, 6), (7, 8)

These teams can also be written as (5, 6), (7, 8), (1, 2), (3, 4) as we don’t have Team #1, Team #2…

We can also solve this question by other method as:

For the first person we can pick a pair in 7 ways;

For the second person one in 5 ways (because 2 people are already chosen above);

For the third person one in 3 ways (because 4 people are already chosen above);

For the fourth one there is only one left.

So, we will get = 7*5*3*1 = 105

Correct Answer: B

Suggested GMAT Quant Questions:

• A Bag Contains 2 White and 3 Red Balls, And a Bag B Contains 4 White and 5 Red Balls
• If n = 3, What is The Value of 2^2n+1?
• If k is an Integer and 2 < k < 7, for How Many Different Values of k is There a Triangle With Sides of Lengths 2, 7, and k?
• If The Average (arithmetic mean) of The Four Numbers 3, 15, 32, and (N + 1) is 18, then N =
• What is the Largest Power of 3 Contained in 200!
• If 30 is Divided by Half and 10 is Added to the Result, Then What is The Final Result?
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes Whereas a leak in the Bottom of the Cistern can Empty a Filled Tank in 40 minutes
• Juan Bought Some Paperback Books That Cost $8 Each and Some Hardcover Books That Cost $25 Each
• What is the value of │x + 7│?
• What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?
• y Varies Directly As x and When x = 6, y = 24. What is the Value of y, When x = 5?
• A Pentagon With 5 Sides Of Equal Length And 5 Interior Angles Of Equal measure is Inscribed in a Circle
• Last Year 26 Members of a Certain Club Traveled to England, 26 Members Traveled to France, and 32 Members Traveled to Italy.
• 4 Out Of 15 Apples Are Rotten. They Are Taken Out One By One At Random
• A is twice as good a workman as B and together they finish a piece of work in 16 days.
• If y u c 0 and j u k 0 Which of the Following Must be True Assuming c kc k
• If 2 98 256L N Where L and N are Integers and 0 N 4 What is the Value of N
• What is the Area of the Triangle with the following Vertices L 1 3 M 5 1 and N 3 5
• If a b and c are distinct positive integers is a by b by c an integer
• If g is an integer what is the value of 1 sq g sq 4 minus 1