Thread: permutation and combination

There are 2 rows of chairs . The first row has 2 chairs and the second row has 4 chairs . In how many ways can 6 people be seated if a couple from the group must sit in the same row ?


THanks in advance

if couple sits in row containing 2 chairs then they can arrange themselves in 2! ways and the rest of the 4 people can arrangethemselves in 4! ways i.e the 6 persons can sit in 2! X 4! ways.

if they coose to sit in row containing 4 chairs then they can arrange themselves in 4X3=12 ways and the rest of the 4 persons can arrange themselves in 4! ways.i.e the 6persons can arrange themselves in 12X4! ways.

Therefore,total no.of ways=2!X4!+12X4!=14X4!=336ways