00:01
In this problem let us look at the first part first we have four brothers and three sisters and the three sisters have to come together so sisters b s1 s2 s3 they have one entity that always come together and the remaining entities are for the boys b1 b2 b3 and b4 so we have five entities in total one each for one boy the brother and one in total for the three three sisters that come together.
00:34
So the number of ways that this can be arranged is simply 5 factorial, which is 120.
00:42
Now let's look at part b.
00:44
Now we want such that no two sisters sit together.
00:50
So let us make the boy brothers sit once.
00:53
So b1 then there has to be a space b2, space b3 space b4, space here and a space here.
01:04
So out of these five spaces, one, two, three, four, and five, the girls, the sisters can sit anywhere.
01:17
So out of these five spaces, first we will choose three spaces for the sisters to sit.
01:24
So that can be done using 5c3.
01:27
Now those three sisters can be internally arranged using 3 factorial...