In how many different ways can a group of six students be equally

Question

In how many different ways can a group of six students be equally distributed into three classes: physics, mathematics and history ?

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

gmatophobia · Accepted Answer

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

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

n = y * x

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

Number of ways =  \frac{6! }{ (2!)^3 }  = 90

Option E

Bunuel · Answer

Similar question to practice: https://gmatclub.com/forum/a-group-of-s ... 02952.html Do you see the difference between these two ?

Bunuel · Answer

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

gmatophobia · Answer

There are 6 students, we can select two students for physics class in 6C2 ways.

As two students have been selected we have 4 students left, two student can be selected for mathematics class in 4C2 ways

As four students have been selected we have two students who can be selected for history class in 2C2 ways

Total = 6C2 * 4C2 * 2C2 =  \frac{6*5 }{ 2*1} * \frac{4*3}{2*1} * \frac{2 * 1}{2*1
}  =  \frac{6! }{ (2!)^3}

Total = 90 ways

AnuK2222 · Answer

hi, why are we not considering the order in which classes are alloted students?

GGGMAT2 · Answer

Here the groups (i.e. classes) are distinct, hence the order is relevant.

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