harithakishore wrote:

But these 4 chosen couples can send two persons (either husband or wife): 2*2*2*2

Bunuel,can you please..please explain this..im confused....

4 chosen couples...i think we can choose 4 different people and not couples..im really confused and also how come it is 2*2*2*2...please explain

We have 6 couples:

A (a_1, a_2);

B (b_1, b_2);

C (c_1, c_2);

D (d_1, d_2);

E (e_1, e_2);

F (f_1, f_2);

We should choose 4 people so that none of them will be married to each other.

The above means that 4 chosen people will be from 4 different couples, for example from A, B, C, D or from A, D, E, F...

The # of ways to choose from which 4 couples these 4 people will be is

C^4_6=15;

Let's consider one particular group of 4 couples: {A, B, C, D}. Now, from couple A in the group could be either

a_1 or

a_2, from couple B in the group could be either

b_1 or

b_2, from couple C in the group could be either

c_1 or

c_2, and from couple D in the group could be either

d_1 or

d_2. So each couple has two options (each couple can be represented in the group of 4 people by

x_1 or

x_2), so one particular group of 4 couples {A, B, C, D} can give us

2*2*2*2=2^4 groups of 4 people from different couples.

One particular group of 4 couples {A, B, C, D} gives

2^4 groups of 4 people from different couples --> 15 groups give

15*2^4 groups of 4 people from different couples (total # of ways to choose 4 people so that no two will be from the same couple) .

Hope it's clear.

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