Question

a family has 4 brother and three sisters is to be arranged in one row.In how many ways can they be seated if no two sisters sit together​

Answer 1

Let the arrangement be *H*H*H*H*

"*" denotes a seat occupied by a sister or a null seat.

*can not hold more than one sister. (pun intended)

from diagram *H*H*H*H* we known that

The first sister has 5 options ,the second sister has 4 options and the third sister has 3 options.

The brothers can interchange in 4! ways.

So total number of ways is

4! x 5 x 4 x 3 = 1440 ways.