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

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- October 11th 2008, 03:01 AMmathaddictpermutation 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 - October 11th 2008, 08:42 AMpankaj
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