Four couples are to be seated in a straight line in such a way that the couples sit together. In how many ways can this be done?

Answer 1

Well suppose the couples are A, B, C, D.

Then we can arrange the couples in 4 x 3 x 2 x 1 = 24 ways.

For one such arrangement eg A B C D, we can arrange the people within the couples in 2 x 2 x 2 x 2 = 16 ways

Why ?

Within couple A we have 2 people, X and Y

they can sit XY or YX (2 ways). Same idea for the other 3 couples.

So total ways = 24 x 16