A group of six friends want to play paintball game. In how many

Question

A group of six friends want to play paintball game. In how many different ways can the group be divided into 3 teams of 2 people each?

(A) 6
(B) 15
(C) 20
(D) 45
(E) 90

Bunuel · Answer

Similar question to practice: https://gmatclub.com/forum/in-how-many- ... 02951.html Do you see the difference between these two ?

gmatophobia · Answer

The groups are identical. The number of ways of arranging "n" people into "y" identical groups consisting of "x" members in each group is given by -

\frac{n ! }{ (x!)^y * y!}

n = y * x

In this case n = 6
y = 3
x = 2

Number of ways =  \frac{6! }{ (2!)^3 * 3!}  = 15

Option B

Bunuel · Answer

How would you solve if you did not know the formula?

gmatophobia · Answer

Three teams need to be formed as shown.

_ _ _

We have six students, two students can be selected in 6C2 ways.

As two students are selected, from the remaining four we can select another set of two students in 4C2 ways.

The last set can be selected in 4C2 ways.

So total ways of selecting = 6C2 * 4C2 * 2C2 ways =  \frac{6*5 }{ 2*1} * \frac{4*3}{2*1} * \frac{2 * 1}{2*1
}  =  \frac{6! }{ (2!)^3}

However note, that the three groups/teams are identical hence the arrangement doesn't matter so we have to de arrange them in  \frac{1 }{ 3!}  ways

Total =  \frac{6! }{ (2!)^3}  *  \frac{1}{3!}  = 15 ways

Adarsh_24 · Answer

Oh I see. In the other question there was distinction between groups - Physics, Maths and History. Here there is no such distinction. So here needs divide by 3!.

Great detail and grouping of questions to show distinction.

Saviooo · Answer

let the 6members be: A B C D E F

We have six students, two students can be selected in 6C2 ways for the first group
And 4C2 ways for the second group and 2C2 for the third.

So total ways of selecting = 6C2 * 4C2 * 2C2 ways = 15*6*1 = 90

but, here the groups are identical, AB in group one is similar to AB in group2 or in group3, so we must divide by 3!

therefore, 90/3! = 15

Option B

A group of six friends want to play paintball game. In how many

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GMAT Problem Solving (PS) Questions

A group of six friends want to play paintball game. In how many

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